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(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(from(X)) → mark(cons(X, from(s(X))))
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active(2ndspos(0, Z)) → mark(rnil)
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active(2ndspos(s(N), cons(X, cons(Y, Z)))) → mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
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active(2ndsneg(0, Z)) → mark(rnil)
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active(2ndsneg(s(N), cons(X, cons(Y, Z)))) → mark(rcons(negrecip(Y), 2ndspos(N, Z)))
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active(pi(X)) → mark(2ndspos(X, from(0)))
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active(plus(0, Y)) → mark(Y)
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active(plus(s(X), Y)) → mark(s(plus(X, Y)))
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active(times(0, Y)) → mark(0)
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active(times(s(X), Y)) → mark(plus(Y, times(X, Y)))
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active(square(X)) → mark(times(X, X))
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active(s(X)) → s(active(X))
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active(posrecip(X)) → posrecip(active(X))
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active(negrecip(X)) → negrecip(active(X))
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active(cons(X1, X2)) → cons(active(X1), X2)
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active(rcons(X1, X2)) → rcons(active(X1), X2)
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active(rcons(X1, X2)) → rcons(X1, active(X2))
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active(from(X)) → from(active(X))
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active(2ndspos(X1, X2)) → 2ndspos(active(X1), X2)
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active(2ndspos(X1, X2)) → 2ndspos(X1, active(X2))
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active(2ndsneg(X1, X2)) → 2ndsneg(active(X1), X2)
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active(2ndsneg(X1, X2)) → 2ndsneg(X1, active(X2))
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active(pi(X)) → pi(active(X))
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active(plus(X1, X2)) → plus(active(X1), X2)
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active(plus(X1, X2)) → plus(X1, active(X2))
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active(times(X1, X2)) → times(active(X1), X2)
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active(times(X1, X2)) → times(X1, active(X2))
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active(square(X)) → square(active(X))
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s(mark(X)) → mark(s(X))
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posrecip(mark(X)) → mark(posrecip(X))
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negrecip(mark(X)) → mark(negrecip(X))
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cons(mark(X1), X2) → mark(cons(X1, X2))
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rcons(mark(X1), X2) → mark(rcons(X1, X2))
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rcons(X1, mark(X2)) → mark(rcons(X1, X2))
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from(mark(X)) → mark(from(X))
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2ndspos(mark(X1), X2) → mark(2ndspos(X1, X2))
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2ndspos(X1, mark(X2)) → mark(2ndspos(X1, X2))
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2ndsneg(mark(X1), X2) → mark(2ndsneg(X1, X2))
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2ndsneg(X1, mark(X2)) → mark(2ndsneg(X1, X2))
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pi(mark(X)) → mark(pi(X))
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plus(mark(X1), X2) → mark(plus(X1, X2))
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plus(X1, mark(X2)) → mark(plus(X1, X2))
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times(mark(X1), X2) → mark(times(X1, X2))
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times(X1, mark(X2)) → mark(times(X1, X2))
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square(mark(X)) → mark(square(X))
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proper(0) → ok(0)
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proper(s(X)) → s(proper(X))
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proper(posrecip(X)) → posrecip(proper(X))
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proper(negrecip(X)) → negrecip(proper(X))
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proper(nil) → ok(nil)
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proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
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proper(rnil) → ok(rnil)
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proper(rcons(X1, X2)) → rcons(proper(X1), proper(X2))
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proper(from(X)) → from(proper(X))
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proper(2ndspos(X1, X2)) → 2ndspos(proper(X1), proper(X2))
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proper(2ndsneg(X1, X2)) → 2ndsneg(proper(X1), proper(X2))
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proper(pi(X)) → pi(proper(X))
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proper(plus(X1, X2)) → plus(proper(X1), proper(X2))
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proper(times(X1, X2)) → times(proper(X1), proper(X2))
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proper(square(X)) → square(proper(X))
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s(ok(X)) → ok(s(X))
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posrecip(ok(X)) → ok(posrecip(X))
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negrecip(ok(X)) → ok(negrecip(X))
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cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
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rcons(ok(X1), ok(X2)) → ok(rcons(X1, X2))
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from(ok(X)) → ok(from(X))
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2ndspos(ok(X1), ok(X2)) → ok(2ndspos(X1, X2))
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2ndsneg(ok(X1), ok(X2)) → ok(2ndsneg(X1, X2))
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pi(ok(X)) → ok(pi(X))
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plus(ok(X1), ok(X2)) → ok(plus(X1, X2))
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times(ok(X1), ok(X2)) → ok(times(X1, X2))
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square(ok(X)) → ok(square(X))
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top(mark(X)) → top(proper(X))
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top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
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(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
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(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
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ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
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ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
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ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
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ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c, c2, c4, c5, c7, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73
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(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
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(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
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ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
S tuples:
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
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ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c2, c4, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9
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(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
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(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1
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(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s(
z0)) →
c11(
S(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.23
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
477.17/149.23
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
477.17/149.23
SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
477.17/149.23
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
477.17/149.23
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
477.17/149.23
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
477.17/149.23
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
477.17/149.23
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
477.17/149.23
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.23
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
477.17/149.23
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
477.17/149.23
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
477.17/149.23
ACTIVE(from(z0)) → c(S(z0))
477.17/149.23
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
477.17/149.23
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
477.17/149.23
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
477.17/149.23
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
477.17/149.23
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
477.17/149.23
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
477.17/149.23
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
477.17/149.23
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
477.17/149.23
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
477.17/149.23
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.23
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.23
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.23
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.23
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.23
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.23
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.23
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.23
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.23
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.23
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.23
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
477.17/149.23
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.23
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.23
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.23
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.23
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.23
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
477.17/149.23
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.23
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.23
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.23
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.23
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.23
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.23
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.23
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.23
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.23
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
477.17/149.23
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
477.17/149.23
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
477.17/149.23
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
477.17/149.23
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
477.17/149.23
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
477.17/149.23
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
477.17/149.23
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
477.17/149.23
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
477.17/149.23
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
477.17/149.23
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
477.17/149.23
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
477.17/149.23
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
477.17/149.24
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
477.17/149.24
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
477.17/149.24
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
477.17/149.24
SQUARE(mark(z0)) → c55(SQUARE(z0))
477.17/149.24
SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
477.17/149.24
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
477.17/149.24
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
477.17/149.24
ACTIVE(from(z0)) → c(S(z0))
477.17/149.24
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
477.17/149.24
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
477.17/149.24
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11
477.17/149.24
477.17/149.24
(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
posrecip(
z0)) →
c12(
POSRECIP(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
477.17/149.24
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
477.17/149.24
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
477.17/149.24
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
477.17/149.24
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
477.17/149.24
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
477.17/149.24
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
477.17/149.24
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
477.17/149.24
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
477.17/149.24
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
477.17/149.24
FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
477.17/149.24
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
477.17/149.24
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
477.17/149.24
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
477.17/149.24
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
477.17/149.24
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
477.17/149.24
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
477.17/149.24
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
477.17/149.24
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12
477.17/149.24
477.17/149.24
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
negrecip(
z0)) →
c13(
NEGRECIP(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
477.17/149.24
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
477.17/149.24
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
477.17/149.24
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
477.17/149.24
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
477.17/149.24
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
477.17/149.24
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.24
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
477.17/149.24
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
477.17/149.24
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
477.17/149.24
ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
477.17/149.24
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
477.17/149.24
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
477.17/149.24
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
477.17/149.24
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.24
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.24
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.24
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.24
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.24
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.24
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13
477.17/149.24
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(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
cons(
z0,
z1)) →
c14(
CONS(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
477.17/149.24
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
477.17/149.24
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.24
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.24
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
477.17/149.24
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
477.17/149.24
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
477.17/149.24
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
477.17/149.24
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
477.17/149.24
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
477.17/149.24
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14
477.17/149.26
477.17/149.26
(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
from(
z0)) →
c17(
FROM(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.26
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.26
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.26
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.26
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.26
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.26
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.26
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.26
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.26
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.26
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.26
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.26
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.26
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.26
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.26
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
477.17/149.26
477.17/149.26
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
477.17/149.26
active(2ndsneg(0, z0)) → mark(rnil)
477.17/149.26
active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
477.17/149.26
active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
477.17/149.26
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
477.17/149.26
pi(mark(z0)) → mark(pi(z0))
477.17/149.26
pi(ok(z0)) → ok(pi(z0))
477.17/149.26
plus(mark(z0), z1) → mark(plus(z0, z1))
477.17/149.26
plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
477.17/149.26
proper(s(z0)) → s(proper(z0))
477.17/149.26
proper(posrecip(z0)) → posrecip(proper(z0))
477.17/149.26
proper(negrecip(z0)) → negrecip(proper(z0))
477.17/149.26
proper(nil) → ok(nil)
477.17/149.26
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
477.17/149.26
proper(rnil) → ok(rnil)
477.17/149.26
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
477.17/149.26
proper(from(z0)) → from(proper(z0))
477.17/149.26
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
477.17/149.26
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
477.17/149.26
proper(pi(z0)) → pi(proper(z0))
477.17/149.26
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
477.17/149.26
proper(times(z0, z1)) → times(proper(z0), proper(z1))
477.17/149.26
proper(square(z0)) → square(proper(z0))
477.17/149.26
top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
477.17/149.26
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
477.17/149.26
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
477.17/149.26
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
477.17/149.26
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
477.17/149.26
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
477.17/149.26
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
477.17/149.26
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.28
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.28
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.28
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
477.17/149.28
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.28
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.28
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
477.17/149.28
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
477.17/149.28
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
477.17/149.28
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.28
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
477.17/149.28
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.28
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17
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(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
pi(
z0)) →
c22(
PI(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.28
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
477.17/149.28
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.28
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.28
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.28
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.28
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.28
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.28
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
477.17/149.28
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.28
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
477.17/149.28
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.28
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.28
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.28
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.28
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
477.17/149.28
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.28
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
477.17/149.28
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.28
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.28
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.28
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.28
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.28
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
477.17/149.28
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.28
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.28
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.28
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.28
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.28
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22
477.17/149.28
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(19) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
square(
z0)) →
c27(
SQUARE(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.28
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.28
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.28
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.29
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.29
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.29
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.29
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.29
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.29
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.29
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.29
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.29
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.29
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.29
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.29
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.29
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.29
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.17/149.29
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.17/149.29
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
477.17/149.29
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
477.17/149.29
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
477.17/149.29
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.29
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.29
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.29
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.29
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.29
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.17/149.29
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
477.17/149.29
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.17/149.29
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
477.17/149.29
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.17/149.29
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
477.17/149.29
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.17/149.29
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
477.17/149.29
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
477.17/149.29
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.17/149.29
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.17/149.29
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.17/149.29
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.17/149.29
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.17/149.29
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
477.17/149.29
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
477.17/149.29
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.17/149.29
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.17/149.29
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.17/149.29
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
477.17/149.29
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.17/149.29
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.17/149.29
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.53/149.30
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.53/149.30
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
477.53/149.30
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
477.53/149.30
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
477.53/149.30
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
477.53/149.30
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
477.53/149.30
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
477.53/149.30
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
477.53/149.30
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
477.53/149.30
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
477.53/149.30
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
477.53/149.30
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
477.53/149.30
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
477.53/149.30
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
477.53/149.30
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
477.53/149.30
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
477.53/149.30
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
477.53/149.30
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
477.53/149.30
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
477.53/149.30
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
477.53/149.30
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
477.53/149.30
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
477.53/149.30
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
477.53/149.30
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
477.53/149.30
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
477.53/149.30
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
477.53/149.30
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
477.53/149.30
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27
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(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c58(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58
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(23) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58
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(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
posrecip(
z0)) →
c59(
POSRECIP(
proper(
z0)),
PROPER(
z0)) by
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.10/149.76
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.10/149.76
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.80
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.80
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59
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(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59
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(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
negrecip(
z0)) →
c60(
NEGRECIP(
proper(
z0)),
PROPER(
z0)) by
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.84
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.84
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.84
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.84
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.84
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.84
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
479.49/149.84
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.84
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.49/149.84
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.49/149.84
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.49/149.84
S(mark(z0)) → c28(S(z0))
479.49/149.84
S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.49/149.84
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.49/149.84
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60
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(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.84
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.84
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.84
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.84
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.84
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.84
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.84
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.84
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.84
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.84
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.84
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.84
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.84
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.84
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.84
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.84
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.84
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.84
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.84
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.84
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.84
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.84
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.84
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.84
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.84
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.84
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.84
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.84
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.84
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.84
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.84
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.84
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.84
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.84
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.84
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.84
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.84
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.84
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.84
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.84
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.84
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.84
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.84
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.84
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.84
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60
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(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons(
z0,
z1)) →
c62(
CONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.85
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.85
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.85
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.85
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.85
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.85
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.85
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.85
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.85
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.85
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.85
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.85
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.85
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.85
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.85
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.85
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.85
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.85
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.85
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.85
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.85
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.85
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.85
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.85
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.85
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.85
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.85
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.85
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.85
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.85
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.85
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.85
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.85
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.49/149.85
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.85
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.85
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.85
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.49/149.85
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.85
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.85
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.85
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.85
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.85
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.85
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.85
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.85
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.85
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.85
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.85
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.85
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.85
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
479.49/149.85
ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.85
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.85
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62
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(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.85
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.85
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.85
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.85
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.85
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.85
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.85
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.85
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.85
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.85
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.85
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.85
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.85
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.85
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.85
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.85
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.85
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.85
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.85
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.85
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.85
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.85
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.85
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.85
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.85
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.85
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.85
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62
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(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
rcons(
z0,
z1)) →
c64(
RCONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.85
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.85
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.86
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.86
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.86
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.86
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.86
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.86
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.86
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.86
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.86
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.49/149.86
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.49/149.86
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.49/149.86
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.49/149.86
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.49/149.86
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.49/149.86
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.86
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.49/149.86
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.49/149.86
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.49/149.86
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.49/149.86
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
479.49/149.86
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
479.49/149.86
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
479.49/149.86
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.86
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.86
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
479.49/149.86
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.86
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.86
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64
479.49/149.86
479.49/149.86
(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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479.49/149.86
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
479.49/149.86
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.86
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.86
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.86
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.86
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.86
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.86
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.86
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.86
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.86
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.86
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.86
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.49/149.86
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.49/149.86
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.49/149.86
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
479.49/149.86
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
479.49/149.86
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
479.49/149.86
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.86
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.49/149.86
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
479.49/149.86
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
479.49/149.86
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.86
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.86
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.86
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.86
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.86
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.86
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.86
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.86
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.86
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.86
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.86
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.86
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.86
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.86
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.86
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.86
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.86
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.86
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.86
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.86
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.86
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.86
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.86
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.86
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.86
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.86
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.86
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.86
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.86
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.86
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.86
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.86
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.86
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.86
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.86
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.86
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.86
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.86
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.86
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.86
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.86
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.86
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.86
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.86
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.86
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.86
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.86
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.86
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.86
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.86
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.86
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.86
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.86
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64
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(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
from(
z0)) →
c65(
FROM(
proper(
z0)),
PROPER(
z0)) by
PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.87
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.87
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.87
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.87
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.87
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.87
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.87
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.87
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.87
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.87
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.87
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.87
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.87
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.87
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.87
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.87
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.87
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.87
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.87
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.87
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.87
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.87
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.87
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.87
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.87
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.87
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.87
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.87
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.87
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.87
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
479.49/149.87
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
479.49/149.87
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
479.49/149.87
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.87
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.49/149.87
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.49/149.87
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.49/149.87
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.49/149.87
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.49/149.87
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.49/149.87
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.49/149.87
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.49/149.87
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.49/149.87
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.49/149.87
S(mark(z0)) → c28(S(z0))
479.49/149.87
S(ok(z0)) → c29(S(z0))
479.49/149.87
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
479.49/149.87
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
479.49/149.87
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
479.49/149.87
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
479.49/149.87
CONS(mark(z0), z1) → c34(CONS(z0, z1))
479.49/149.87
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.49/149.87
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.49/149.87
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
479.49/149.87
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
479.49/149.87
FROM(mark(z0)) → c39(FROM(z0))
479.49/149.87
FROM(ok(z0)) → c40(FROM(z0))
479.49/149.87
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
479.49/149.87
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.87
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.87
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.87
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.87
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.87
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.87
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.87
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.87
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.87
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.87
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.87
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.87
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.87
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.87
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.87
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.87
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.87
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.87
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.87
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.87
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.87
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.87
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.87
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.87
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.87
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.87
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.87
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.87
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.87
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65
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(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.87
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.87
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.87
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.87
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.87
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.87
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.87
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.87
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.87
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.87
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.87
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.87
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.87
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.87
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.87
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.87
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.87
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.87
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.87
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.87
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.87
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.87
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.87
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.87
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.87
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.87
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.87
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.87
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.87
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.87
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.87
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.87
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.87
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.87
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.87
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.87
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.87
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.87
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.87
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.87
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.87
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.87
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.87
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.87
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.87
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.87
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.87
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.87
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.87
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.87
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.87
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.87
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.87
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.87
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.87
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.87
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.87
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.87
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.87
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.87
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.87
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.87
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.87
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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PROPER(from(0)) → c65(FROM(ok(0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.87
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
479.49/149.87
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
479.49/149.87
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
479.49/149.87
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.87
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
479.49/149.87
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
479.49/149.87
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
479.49/149.87
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
479.49/149.87
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.49/149.87
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
479.49/149.87
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.49/149.87
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.49/149.87
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
479.49/149.87
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
479.49/149.87
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.88
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.88
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.88
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.88
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.88
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.88
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.88
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.88
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.88
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.88
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.88
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.88
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.88
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.88
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.88
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(from(0)) → c65(FROM(ok(0)))
479.49/149.88
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.49/149.88
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65
479.49/149.88
479.49/149.88
(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
2ndspos(
z0,
z1)) →
c66(
2NDSPOS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.49/149.88
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.49/149.88
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.49/149.88
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.49/149.88
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.49/149.88
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.49/149.88
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
479.49/149.88
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
479.49/149.88
active(2ndspos(0, z0)) → mark(rnil)
479.49/149.88
active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
479.49/149.88
active(2ndsneg(0, z0)) → mark(rnil)
479.49/149.88
active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
479.49/149.88
active(pi(z0)) → mark(2ndspos(z0, from(0)))
479.49/149.88
active(plus(0, z0)) → mark(z0)
479.49/149.88
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
479.49/149.88
active(times(0, z0)) → mark(0)
479.49/149.88
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
479.49/149.88
active(square(z0)) → mark(times(z0, z0))
479.49/149.88
active(s(z0)) → s(active(z0))
479.49/149.88
active(posrecip(z0)) → posrecip(active(z0))
479.49/149.88
active(negrecip(z0)) → negrecip(active(z0))
479.49/149.88
active(cons(z0, z1)) → cons(active(z0), z1)
479.49/149.88
active(rcons(z0, z1)) → rcons(active(z0), z1)
479.49/149.88
active(rcons(z0, z1)) → rcons(z0, active(z1))
479.49/149.88
active(from(z0)) → from(active(z0))
479.49/149.88
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
479.49/149.88
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
479.49/149.88
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.88
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.88
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.88
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.88
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.88
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.88
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.88
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.88
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.88
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.88
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.88
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.88
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.88
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.88
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.88
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.88
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(from(0)) → c65(FROM(ok(0)))
479.49/149.88
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.49/149.88
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.49/149.88
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.49/149.88
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.49/149.88
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.49/149.88
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.49/149.88
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.49/149.88
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.49/149.88
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.88
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.49/149.88
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.49/149.88
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.49/149.88
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.49/149.88
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.49/149.88
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.49/149.88
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.49/149.88
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.49/149.88
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.49/149.88
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.49/149.88
S(mark(z0)) → c28(S(z0))
479.49/149.88
S(ok(z0)) → c29(S(z0))
479.49/149.88
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
479.49/149.88
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
479.49/149.88
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
479.49/149.88
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
479.49/149.88
CONS(mark(z0), z1) → c34(CONS(z0, z1))
479.49/149.88
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.49/149.88
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.49/149.88
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
479.49/149.88
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.49/149.88
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.49/149.88
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.88
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.88
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.88
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(s(0)) → c58(S(ok(0)))
479.49/149.88
PROPER(s(nil)) → c58(S(ok(nil)))
479.49/149.88
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.88
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.49/149.88
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.88
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.49/149.88
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.88
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.88
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.88
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.88
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.88
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.88
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.88
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.88
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.88
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.88
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.88
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.88
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.88
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.88
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.88
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.88
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.88
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.88
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.88
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.88
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.88
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.88
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.88
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.88
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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PROPER(from(0)) → c65(FROM(ok(0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66
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(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.88
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.88
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.88
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.88
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.49/149.88
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.88
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.88
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.49/149.88
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.88
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.88
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.88
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.88
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.89
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.89
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.89
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.89
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.89
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.89
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.89
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.89
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.89
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.89
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.89
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.49/149.89
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.89
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.49/149.89
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.89
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.49/149.89
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.89
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.89
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.89
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.89
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
479.49/149.89
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.49/149.89
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.89
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.49/149.89
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.89
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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PROPER(from(0)) → c65(FROM(ok(0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
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PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.49/149.89
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.89
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.89
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.49/149.89
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.49/149.89
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.49/149.89
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.49/149.89
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.89
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.49/149.89
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.49/149.89
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.49/149.89
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.49/149.89
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.49/149.89
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.49/149.89
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.49/149.89
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.49/149.89
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.49/149.89
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.49/149.89
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.49/149.89
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.89
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.49/149.89
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.49/149.89
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.89
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.89
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.89
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.89
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.89
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.89
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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PROPER(from(0)) → c65(FROM(ok(0)))
479.49/149.89
PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
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PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66
479.49/149.89
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(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
2ndsneg(
z0,
z1)) →
c67(
2NDSNEG(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.49/149.89
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.89
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.89
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.89
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.89
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.89
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.89
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.89
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.89
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.89
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.49/149.89
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.49/149.89
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.49/149.89
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.49/149.89
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.49/149.89
PROPER(from(0)) → c65(FROM(ok(0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
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PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.49/149.89
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.89
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.89
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.49/149.89
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.49/149.89
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.49/149.89
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.89
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.89
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.89
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.89
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.89
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.89
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.49/149.89
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.49/149.89
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.49/149.89
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
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PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.49/149.89
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.49/149.89
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.49/149.89
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.49/149.89
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
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PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
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PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
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PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
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PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.90
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.49/149.90
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.90
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.49/149.90
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.49/149.90
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.49/149.90
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.49/149.90
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.49/149.90
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.49/149.90
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.49/149.90
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.49/149.90
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.49/149.90
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.49/149.90
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.49/149.90
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.49/149.90
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.49/149.90
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.49/149.90
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.49/149.90
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.49/149.90
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.49/149.90
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.49/149.90
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
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PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
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PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
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PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
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PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
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PROPER(from(0)) → c65(FROM(ok(0)))
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PROPER(from(nil)) → c65(FROM(ok(nil)))
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PROPER(from(rnil)) → c65(FROM(ok(rnil)))
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PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67
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(51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
479.76/149.90
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.90
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.90
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.90
PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.90
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.90
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.90
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.90
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.90
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.90
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.90
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.90
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.90
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.90
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.90
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.90
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.90
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.90
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.90
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.90
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.90
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.90
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.90
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.90
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.90
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.90
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.90
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.90
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.90
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.90
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.90
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.90
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.90
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.90
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.90
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.90
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.90
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.90
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.90
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.90
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.90
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.90
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.90
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.90
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.90
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.90
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.90
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.90
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.90
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.90
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.90
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.90
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.90
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.90
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.90
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.90
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.90
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.90
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.90
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.90
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.90
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.90
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.90
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.90
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.90
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67
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(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
pi(
z0)) →
c68(
PI(
proper(
z0)),
PROPER(
z0)) by
PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
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PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
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PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
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PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
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PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
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PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
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(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.91
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.91
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.91
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.91
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.91
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.91
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.91
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.91
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.91
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.91
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.91
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.91
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.91
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.91
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
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PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
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PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
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PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
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PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
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PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.91
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.91
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.91
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.91
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.91
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.91
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.91
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.91
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.91
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.91
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.91
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.91
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.91
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.91
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.91
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.91
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.91
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
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PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
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PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
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PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
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PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
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PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68
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(55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.91
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.91
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.91
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.91
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.91
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.91
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.91
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.91
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.91
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.91
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.91
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.91
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.91
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.91
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.91
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.91
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.91
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.91
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.91
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.91
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.91
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.91
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.91
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.91
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.91
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.91
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.91
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.91
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.91
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.91
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.91
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.91
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.91
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.91
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.91
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.91
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.91
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.91
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.91
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.91
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.91
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.91
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.91
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.91
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.91
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.91
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.91
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.91
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.91
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.91
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.91
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.91
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.91
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.91
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.91
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.91
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.91
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.91
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.91
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.91
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.91
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.91
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.91
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.91
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.91
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.91
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.91
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.91
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.91
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.91
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.76/149.91
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.76/149.91
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.76/149.91
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.76/149.91
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.76/149.91
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.76/149.91
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.76/149.91
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.76/149.91
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.76/149.91
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.76/149.91
S(mark(z0)) → c28(S(z0))
479.76/149.91
S(ok(z0)) → c29(S(z0))
479.76/149.91
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
479.76/149.91
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
479.76/149.91
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
479.76/149.91
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
479.76/149.91
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.76/149.91
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.76/149.91
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
479.76/149.91
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
479.76/149.91
FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
479.76/149.91
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
479.76/149.91
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
479.76/149.91
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
479.76/149.91
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.92
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.92
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.92
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.92
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.92
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.92
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.92
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.92
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.92
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.92
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.92
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.92
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.92
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.92
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.92
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.92
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.92
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.92
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.92
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.92
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.92
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.92
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.92
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.92
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.92
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.92
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.92
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.92
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.92
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.92
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.92
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.92
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.92
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.92
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.92
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.92
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68
479.76/149.92
479.76/149.92
(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
plus(
z0,
z1)) →
c69(
PLUS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.76/149.92
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.76/149.92
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.76/149.92
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.92
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.92
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.92
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.92
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.92
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.92
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.92
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.92
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.92
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.92
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.92
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.92
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.92
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.92
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.92
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.76/149.92
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.76/149.92
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.76/149.92
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.76/149.92
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.76/149.92
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.76/149.92
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.92
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.76/149.92
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.76/149.92
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.76/149.92
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.76/149.92
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.76/149.92
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.76/149.92
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.76/149.92
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.76/149.92
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.76/149.92
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.76/149.92
S(mark(z0)) → c28(S(z0))
479.76/149.92
S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.76/149.92
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.76/149.92
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
479.76/149.92
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
479.76/149.92
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
479.76/149.92
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
479.76/149.92
PI(mark(z0)) → c47(PI(z0))
479.76/149.92
PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
479.76/149.92
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
479.76/149.92
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
479.76/149.92
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
479.76/149.92
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
479.76/149.92
SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
479.76/149.92
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
479.76/149.92
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
479.76/149.92
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
479.76/149.92
ACTIVE(from(z0)) → c(S(z0))
479.76/149.92
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
479.76/149.92
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
479.76/149.92
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
479.76/149.92
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
479.76/149.92
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
479.76/149.92
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.92
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.92
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.92
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.92
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.92
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.92
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.92
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.92
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.92
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.92
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.92
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.92
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.92
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.92
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.92
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.92
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.92
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.92
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.92
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.92
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.92
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.92
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.92
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.92
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.92
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.92
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.92
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.92
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.92
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.92
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.92
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.92
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.92
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.92
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.92
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.92
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.92
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.92
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.92
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.92
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.92
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
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PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.92
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.92
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.92
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.92
PROPER(pi(0)) → c68(PI(ok(0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
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PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.76/149.92
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.92
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.92
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.92
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.76/149.92
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.92
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.76/149.92
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.92
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.92
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.92
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.92
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.92
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.92
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.92
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.92
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69
479.76/149.93
479.76/149.93
(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
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PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
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PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.93
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.93
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.93
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.93
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.93
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.93
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.93
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.93
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.93
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
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PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
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PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
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PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
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PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
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PROPER(pi(0)) → c68(PI(ok(0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
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PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.93
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.93
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.93
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.93
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.93
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.93
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.93
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.93
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.93
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.93
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.93
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.93
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.93
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.93
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.93
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.93
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.93
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.93
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.93
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.93
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.93
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.93
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.93
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.93
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.93
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.93
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.93
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.93
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.93
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.93
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.93
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.93
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.93
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.93
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.93
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.93
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.93
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.93
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.93
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.93
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.93
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.93
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69
479.76/149.93
479.76/149.93
(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
times(
z0,
z1)) →
c70(
TIMES(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.76/149.93
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.93
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.93
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.93
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.76/149.93
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.76/149.93
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.93
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.93
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.93
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.93
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.76/149.93
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.93
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.93
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.76/149.93
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.76/149.93
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.93
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.93
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
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PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.93
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.93
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.93
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.93
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.93
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.93
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.93
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.93
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.93
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.93
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.93
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.93
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.93
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.93
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.93
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.93
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.93
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.93
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.94
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.94
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.94
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.94
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.94
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.94
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(pi(0)) → c68(PI(ok(0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
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PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
479.76/149.94
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
479.76/149.94
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
479.76/149.94
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
479.76/149.94
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
479.76/149.94
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
479.76/149.94
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.94
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.76/149.94
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.76/149.94
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.76/149.94
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.76/149.94
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.76/149.94
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.76/149.94
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.76/149.94
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.76/149.94
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.76/149.94
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.76/149.94
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
479.76/149.94
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
479.76/149.94
CONS(mark(z0), z1) → c34(CONS(z0, z1))
479.76/149.94
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
479.76/149.94
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
479.76/149.94
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
479.76/149.94
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
479.76/149.94
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
479.76/149.94
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
479.76/149.94
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
479.76/149.94
SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
479.76/149.94
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
479.76/149.94
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.94
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.94
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.94
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.94
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.94
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.94
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.94
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.94
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.94
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.94
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.94
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.94
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.94
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.94
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.94
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.94
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.94
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.94
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.94
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.94
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.94
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.94
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.94
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.94
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.94
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.94
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.94
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.94
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.94
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.94
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.94
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.94
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.94
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.94
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.94
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.94
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
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PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
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PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
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PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
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PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
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PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
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PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70
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(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
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(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.94
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.94
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.94
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.94
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.94
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.94
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.94
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.94
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.94
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.94
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.94
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.94
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.94
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.94
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.94
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.94
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.94
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.94
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.94
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.94
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.94
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.94
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.94
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.94
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.94
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.94
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.94
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.94
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.94
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.94
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.94
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.94
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.94
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.94
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.94
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.94
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.94
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.94
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.94
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.94
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.94
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.94
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.94
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.94
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.94
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.94
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.94
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.94
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.94
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.94
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.94
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.94
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.94
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.94
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.94
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.94
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.94
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.94
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.94
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.94
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.94
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.94
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.94
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.94
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.95
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.95
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.95
PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.95
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.95
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.95
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.95
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.95
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.95
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.95
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.95
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.95
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.95
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
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PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
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PROPER(pi(0)) → c68(PI(ok(0)))
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PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
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PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
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PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70
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(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
square(
z0)) →
c71(
SQUARE(
proper(
z0)),
PROPER(
z0)) by
PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
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PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
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PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
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PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
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PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
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PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
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(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.95
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.95
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.95
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.95
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.95
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.95
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.95
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.95
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.95
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.95
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.95
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.95
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.95
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.95
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.95
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.95
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.95
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.95
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.95
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.95
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.95
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.95
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.95
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
479.76/149.95
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
479.76/149.95
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
479.76/149.95
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.95
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.76/149.95
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.76/149.95
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.76/149.95
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.95
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.95
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.95
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.95
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.95
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.95
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.95
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.95
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.95
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.95
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.95
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.95
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.95
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.95
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.95
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.95
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.95
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.95
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.95
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.95
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.95
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.95
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.95
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.95
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.95
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.95
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.95
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.95
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.95
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.95
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.95
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.95
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.95
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.95
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.95
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.95
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.95
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.95
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.95
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.95
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.96
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.96
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.96
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
479.76/149.96
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
479.76/149.96
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
479.76/149.96
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71
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(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
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PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
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PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.96
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.96
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.96
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.96
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.96
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.96
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.96
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.96
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.96
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.96
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.96
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.96
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.96
PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.96
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(square(0)) → c71(SQUARE(ok(0)))
479.76/149.96
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
479.76/149.96
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.96
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
479.76/149.96
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
479.76/149.96
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
479.76/149.96
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
479.76/149.96
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
479.76/149.96
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
479.76/149.96
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
479.76/149.96
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
479.76/149.96
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
479.76/149.96
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
479.76/149.96
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.96
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.96
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.96
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.96
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.96
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.96
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.96
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.96
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.96
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.96
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.96
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.96
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.96
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.96
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.96
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.96
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.96
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.96
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.96
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.96
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.96
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.96
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.96
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.96
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.96
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.96
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.96
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.96
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.96
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.96
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.96
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.96
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.96
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.96
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.96
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.96
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.96
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.96
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.96
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.96
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.96
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.96
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.96
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.96
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.96
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.96
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.96
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.96
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.96
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.96
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.96
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.96
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.96
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.96
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.96
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.96
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.96
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.96
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.96
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.96
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.96
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.96
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.96
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.96
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.96
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.96
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.96
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.96
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.96
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.96
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.96
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.96
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.96
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.96
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.96
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.96
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.96
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.96
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.96
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.96
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.96
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.96
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.96
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.96
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.96
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.96
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.96
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.96
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.96
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.96
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.96
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.96
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.96
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.96
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.96
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.96
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.96
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.96
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.96
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.96
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.96
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.96
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
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PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
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PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
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PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
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PROPER(square(0)) → c71(SQUARE(ok(0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71
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(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c72(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
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TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
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TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
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TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
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(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.97
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.97
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.97
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.97
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.97
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.97
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.97
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.97
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.97
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.97
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.97
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.97
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.97
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.97
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.97
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.97
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.97
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.97
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.97
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.97
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.97
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.97
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.97
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.97
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.97
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.97
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.97
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.97
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.97
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.97
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.97
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.97
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.97
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.97
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.97
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.97
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.97
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.97
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.97
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.97
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.97
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(square(0)) → c71(SQUARE(ok(0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
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TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
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TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
479.76/149.97
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.97
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
479.76/149.97
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.97
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.97
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.97
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.97
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.97
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
479.76/149.97
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.97
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.97
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.97
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.97
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.97
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.97
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.97
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.97
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.97
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.97
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.97
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.97
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.97
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.97
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.97
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.97
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.97
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.97
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.97
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.97
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.97
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
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PROPER(square(0)) → c71(SQUARE(ok(0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
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TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
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TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
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TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
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TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72
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(71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.97
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.97
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.97
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.97
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.97
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.97
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.97
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.97
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.97
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.97
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.97
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.97
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.97
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.97
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.97
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.97
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.97
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.97
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.97
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.97
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.97
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.97
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.97
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.97
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.97
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.97
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.97
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.97
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.97
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.97
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.97
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.97
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.97
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.97
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.97
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.97
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.98
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.98
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.98
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.98
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.98
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.98
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(square(0)) → c71(SQUARE(ok(0)))
479.76/149.98
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
479.76/149.98
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
479.76/149.98
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
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TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
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TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
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TOP(mark(0)) → c72(TOP(ok(0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
479.76/149.98
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.98
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.98
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.98
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.98
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.98
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.98
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.98
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.98
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.98
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.98
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.98
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.98
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.98
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.98
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.98
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.98
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.98
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.98
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.98
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.98
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.98
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.98
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.98
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.98
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(square(0)) → c71(SQUARE(ok(0)))
479.76/149.98
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
479.76/149.98
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
479.76/149.98
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
TOP(mark(0)) → c72(TOP(ok(0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72
479.76/149.98
479.76/149.98
(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c73(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.98
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.98
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.98
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.98
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
479.76/149.98
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
479.76/149.98
active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
479.76/149.98
active(2ndsneg(0, z0)) → mark(rnil)
479.76/149.98
active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
479.76/149.98
active(pi(z0)) → mark(2ndspos(z0, from(0)))
479.76/149.98
active(plus(0, z0)) → mark(z0)
479.76/149.98
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
479.76/149.98
active(times(0, z0)) → mark(0)
479.76/149.98
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
479.76/149.98
active(square(z0)) → mark(times(z0, z0))
479.76/149.98
active(s(z0)) → s(active(z0))
479.76/149.98
active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
479.76/149.98
active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.98
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.98
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
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PROPER(s(0)) → c58(S(ok(0)))
479.76/149.98
PROPER(s(nil)) → c58(S(ok(nil)))
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PROPER(s(rnil)) → c58(S(ok(rnil)))
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PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
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PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
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PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
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PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.98
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.98
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.98
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.98
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.98
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.98
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.98
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.98
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.98
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.98
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.98
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.98
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.98
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.98
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.98
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.98
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.98
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.98
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.98
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.98
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.98
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.98
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.98
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
479.76/149.98
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
479.76/149.98
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.98
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.98
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
PROPER(square(0)) → c71(SQUARE(ok(0)))
479.76/149.98
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
479.76/149.98
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
479.76/149.98
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
479.76/149.98
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.98
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.98
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.98
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.98
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
479.76/149.98
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.98
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.98
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.98
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.98
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.98
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
479.76/149.98
TOP(mark(0)) → c72(TOP(ok(0)))
479.76/149.98
TOP(mark(nil)) → c72(TOP(ok(nil)))
479.76/149.98
TOP(mark(rnil)) → c72(TOP(ok(rnil)))
479.76/149.98
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.98
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.98
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.98
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.98
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.98
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.98
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.98
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
479.76/149.98
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.98
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.98
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
479.76/149.98
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.98
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.98
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.98
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.98
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.98
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
479.76/149.98
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.98
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.98
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.98
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.98
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.98
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.99
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.99
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.99
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
479.76/149.99
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.99
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
479.76/149.99
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.99
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.99
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.99
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.99
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.99
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.99
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.99
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.99
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.99
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.99
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.99
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.99
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.99
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.99
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.99
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.99
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.99
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.99
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.99
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.99
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.99
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.99
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.99
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.99
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.99
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.99
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.99
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.99
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.99
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.99
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.99
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.99
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.99
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.99
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.99
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.99
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.99
PROPER(pi(nil)) → c68(PI(ok(nil)))
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PROPER(pi(rnil)) → c68(PI(ok(rnil)))
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PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
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PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
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PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
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PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
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PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
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PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
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PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
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PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
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PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
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PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
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PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
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PROPER(square(0)) → c71(SQUARE(ok(0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
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TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
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TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
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TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
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TOP(mark(0)) → c72(TOP(ok(0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)))
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TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
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TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
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TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
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TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
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TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
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TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
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TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73
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(75) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
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ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
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ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
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ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
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ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
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ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
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ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
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ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
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ACTIVE(from(z0)) → c(S(z0))
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ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
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ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
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ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
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ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
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ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
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ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
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ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
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ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
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ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
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ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
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ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
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ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
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ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
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ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
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ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
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ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
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ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
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ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
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ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
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ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
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ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
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ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.99
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.99
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.99
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
479.76/149.99
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.99
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
479.76/149.99
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.99
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.99
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.99
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
479.76/149.99
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
479.76/149.99
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
479.76/149.99
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
479.76/149.99
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
479.76/149.99
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
479.76/149.99
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
479.76/149.99
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
479.76/149.99
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
479.76/149.99
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
479.76/149.99
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
479.76/149.99
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
479.76/149.99
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
479.76/149.99
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
479.76/149.99
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
479.76/149.99
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
479.76/149.99
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
479.76/149.99
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
479.76/149.99
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
479.76/149.99
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
479.76/149.99
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(s(0)) → c58(S(ok(0)))
479.76/149.99
PROPER(s(nil)) → c58(S(ok(nil)))
479.76/149.99
PROPER(s(rnil)) → c58(S(ok(rnil)))
479.76/149.99
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
479.76/149.99
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
479.76/149.99
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
479.76/149.99
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
479.76/149.99
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
479.76/149.99
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
479.76/149.99
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(from(0)) → c65(FROM(ok(0)))
479.76/149.99
PROPER(from(nil)) → c65(FROM(ok(nil)))
479.76/149.99
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
479.76/149.99
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
479.76/149.99
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
479.76/149.99
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
479.76/149.99
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
479.76/149.99
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
479.76/149.99
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
479.76/149.99
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
479.76/149.99
PROPER(pi(0)) → c68(PI(ok(0)))
479.76/149.99
PROPER(pi(nil)) → c68(PI(ok(nil)))
479.76/149.99
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
479.76/149.99
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
479.76/149.99
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
479.76/149.99
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
479.76/149.99
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
479.76/149.99
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
479.76/149.99
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
479.76/149.99
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
479.76/149.99
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
479.76/149.99
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
479.76/149.99
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
479.76/149.99
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
479.76/149.99
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
479.76/149.99
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
479.76/149.99
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
479.76/149.99
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
479.76/149.99
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
479.76/149.99
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
479.76/149.99
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
479.76/149.99
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
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PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
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PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
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PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
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PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
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PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
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PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
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PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
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PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
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PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
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PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
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PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
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PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
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PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
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PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
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PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
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PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
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PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
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PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
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PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
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PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
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PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
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PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
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PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
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PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
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PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
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PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
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PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
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PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
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PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
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PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
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PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
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PROPER(square(0)) → c71(SQUARE(ok(0)))
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PROPER(square(nil)) → c71(SQUARE(ok(nil)))
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PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
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TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
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TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
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TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
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TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
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TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
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TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
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TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
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TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
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TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
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TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
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TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
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TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
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TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
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TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
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TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
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TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
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TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
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TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
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TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
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TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
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TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
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TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
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TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
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TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
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TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
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TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
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TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
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TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
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TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
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TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
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TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
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TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
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TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
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TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
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TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
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TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
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TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
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TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
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TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
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TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))
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(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(0)) → c72(TOP(ok(0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(0)) → c72(TOP(ok(0)))
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TOP(mark(nil)) → c72(TOP(ok(nil)))
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TOP(mark(rnil)) → c72(TOP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c72
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(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
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(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(0)) → c72
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TOP(mark(nil)) → c72
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TOP(mark(rnil)) → c72
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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TOP(mark(0)) → c72
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TOP(mark(nil)) → c72
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TOP(mark(rnil)) → c72
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c72
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(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing nodes:
TOP(mark(rnil)) → c72
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TOP(mark(0)) → c72
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TOP(mark(nil)) → c72
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(80) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(81) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = 0
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = 0
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POL(PLUS(x1, x2)) = 0
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POL(POSRECIP(x1)) = x1
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POL(RCONS(x1, x2)) = 0
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = [1] + x1
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(82) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(83) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = 0
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = 0
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POL(PLUS(x1, x2)) = x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = 0
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = [1] + x1
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(84) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(85) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = 0
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = x1
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POL(PLUS(x1, x2)) = x1 + [3]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = 0
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [2] + x1
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POL(ok(x1)) = [1] + x1
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(86) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(87) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = x1
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = 0
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [3]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = 0
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [2] + x1
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POL(ok(x1)) = x1
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(88) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(89) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
FROM(ok(z0)) → c40(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = x1
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [3]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = 0
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = x1
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POL(ok(x1)) = [1] + x1
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(90) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(91) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = x1
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [3]x1 + [3]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = x1
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = 0
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POL(TIMES(x1, x2)) = 0
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = [2] + x1
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(92) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(93) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = 0
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [5]x1 + [3]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = [5]x1
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = x1
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POL(TIMES(x1, x2)) = x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = [2] + x1
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(94) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(95) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [3]x1
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POL(NEGRECIP(x1)) = x1
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [5]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = [5]x1
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [5]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = [1] + x1
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(96) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(97) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = 0
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [3]x1
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POL(NEGRECIP(x1)) = [5]x1
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [3]x1 + [3]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = [5]x1 + x2
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = [5]x1
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POL(TIMES(x1, x2)) = [5]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [2] + x1
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POL(ok(x1)) = x1
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(98) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(99) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = 0
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POL(2NDSPOS(x1, x2)) = x1
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [3]x1
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [3]x1 + [5]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = [3]x1 + [3]x2
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [5]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = x1
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POL(ok(x1)) = [2] + x1
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(100) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(101) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [2]x2
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POL(2NDSPOS(x1, x2)) = x1 + x2
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [3]x1
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [5]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = [3]x1 + [5]x2
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POL(S(x1)) = 0
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [3]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [4] + x1
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POL(ok(x1)) = [1] + x1
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(102) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(103) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
S(mark(z0)) → c28(S(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [5]x1 + [5]x2
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POL(2NDSPOS(x1, x2)) = [5]x1 + [5]x2
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POL(CONS(x1, x2)) = x2
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [5]x1
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [5]x1 + [5]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = [3]x1 + [3]x2
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POL(S(x1)) = [2]x1
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [3]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = x1
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(104) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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S(mark(z0)) → c28(S(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(105) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
S(ok(z0)) → c29(S(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [5]x1 + [3]x2
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POL(2NDSPOS(x1, x2)) = [5]x1 + [5]x2
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POL(CONS(x1, x2)) = 0
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [5]x1
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [5]x1 + [3]x2
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POL(POSRECIP(x1)) = [5]x1
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POL(RCONS(x1, x2)) = [3]x1 + [3]x2
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POL(S(x1)) = [2]x1
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [3]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = x1
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POL(ok(x1)) = [1] + x1
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(106) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(107) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS(mark(z0), z1) → c34(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [5]x1 + [5]x2
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POL(2NDSPOS(x1, x2)) = [3]x1 + [3]x2
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POL(CONS(x1, x2)) = [2]x1
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [3]x1
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [5]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = [3]x1 + [5]x2
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POL(S(x1)) = [3]x1
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POL(SQUARE(x1)) = [3]x1
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POL(TIMES(x1, x2)) = [3]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = x1
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(108) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(109) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [5]x1 + [5]x2
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POL(2NDSPOS(x1, x2)) = [3]x1 + [5]x2
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POL(CONS(x1, x2)) = x2
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [5]x1
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POL(PI(x1)) = [5]x1
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POL(PLUS(x1, x2)) = [3]x1 + [5]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = [5]x1 + [5]x2
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POL(S(x1)) = [3]x1
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POL(SQUARE(x1)) = [5]x1
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POL(TIMES(x1, x2)) = [5]x1
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [5] + x1
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POL(ok(x1)) = [1] + x1
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(110) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(111) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
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POL(2NDSNEG(x1, x2)) = [5]x1 + [3]x2
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POL(2NDSPOS(x1, x2)) = [3]x1 + [3]x2
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POL(CONS(x1, x2)) = [3]x1 + [3]x2
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POL(FROM(x1)) = [5]x1
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POL(NEGRECIP(x1)) = [3]x1
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POL(PI(x1)) = [3]x1
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POL(PLUS(x1, x2)) = [3]x1 + [3]x2
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POL(POSRECIP(x1)) = [3]x1
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POL(RCONS(x1, x2)) = [3]x1 + [5]x2
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POL(S(x1)) = [5]x1
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POL(SQUARE(x1)) = [5]x1
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POL(TIMES(x1, x2)) = [5]x1 + [5]x2
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POL(c28(x1)) = x1
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POL(c29(x1)) = x1
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POL(c30(x1)) = x1
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POL(c31(x1)) = x1
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POL(c32(x1)) = x1
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POL(c33(x1)) = x1
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POL(c34(x1)) = x1
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POL(c35(x1)) = x1
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POL(c36(x1)) = x1
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POL(c37(x1)) = x1
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POL(c38(x1)) = x1
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POL(c39(x1)) = x1
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POL(c40(x1)) = x1
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POL(c41(x1)) = x1
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POL(c42(x1)) = x1
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POL(c43(x1)) = x1
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POL(c44(x1)) = x1
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POL(c45(x1)) = x1
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POL(c46(x1)) = x1
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POL(c47(x1)) = x1
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POL(c48(x1)) = x1
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POL(c49(x1)) = x1
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POL(c50(x1)) = x1
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POL(c51(x1)) = x1
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POL(c52(x1)) = x1
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POL(c53(x1)) = x1
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POL(c54(x1)) = x1
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POL(c55(x1)) = x1
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POL(c56(x1)) = x1
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POL(mark(x1)) = [1] + x1
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POL(ok(x1)) = x1
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(112) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
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active(2ndspos(0, z0)) → mark(rnil)
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active(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
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active(2ndsneg(0, z0)) → mark(rnil)
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active(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
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active(pi(z0)) → mark(2ndspos(z0, from(0)))
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active(plus(0, z0)) → mark(z0)
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active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
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active(times(0, z0)) → mark(0)
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active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
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active(square(z0)) → mark(times(z0, z0))
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active(s(z0)) → s(active(z0))
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active(posrecip(z0)) → posrecip(active(z0))
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active(negrecip(z0)) → negrecip(active(z0))
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active(cons(z0, z1)) → cons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(active(z0), z1)
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active(rcons(z0, z1)) → rcons(z0, active(z1))
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active(from(z0)) → from(active(z0))
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active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
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active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
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active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
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active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
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active(pi(z0)) → pi(active(z0))
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active(plus(z0, z1)) → plus(active(z0), z1)
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active(plus(z0, z1)) → plus(z0, active(z1))
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active(times(z0, z1)) → times(active(z0), z1)
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active(times(z0, z1)) → times(z0, active(z1))
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active(square(z0)) → square(active(z0))
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s(mark(z0)) → mark(s(z0))
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s(ok(z0)) → ok(s(z0))
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posrecip(mark(z0)) → mark(posrecip(z0))
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posrecip(ok(z0)) → ok(posrecip(z0))
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negrecip(mark(z0)) → mark(negrecip(z0))
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negrecip(ok(z0)) → ok(negrecip(z0))
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cons(mark(z0), z1) → mark(cons(z0, z1))
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cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
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rcons(mark(z0), z1) → mark(rcons(z0, z1))
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rcons(z0, mark(z1)) → mark(rcons(z0, z1))
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rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
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from(mark(z0)) → mark(from(z0))
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from(ok(z0)) → ok(from(z0))
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2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
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2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
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2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
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2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
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2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
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2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
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pi(mark(z0)) → mark(pi(z0))
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pi(ok(z0)) → ok(pi(z0))
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plus(mark(z0), z1) → mark(plus(z0, z1))
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plus(z0, mark(z1)) → mark(plus(z0, z1))
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plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
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times(mark(z0), z1) → mark(times(z0, z1))
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times(z0, mark(z1)) → mark(times(z0, z1))
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times(ok(z0), ok(z1)) → ok(times(z0, z1))
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square(mark(z0)) → mark(square(z0))
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square(ok(z0)) → ok(square(z0))
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proper(0) → ok(0)
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proper(s(z0)) → s(proper(z0))
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proper(posrecip(z0)) → posrecip(proper(z0))
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proper(negrecip(z0)) → negrecip(proper(z0))
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proper(nil) → ok(nil)
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proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
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proper(rnil) → ok(rnil)
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proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
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proper(from(z0)) → from(proper(z0))
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proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
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proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
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proper(pi(z0)) → pi(proper(z0))
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proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
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proper(times(z0, z1)) → times(proper(z0), proper(z1))
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proper(square(z0)) → square(proper(z0))
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top(mark(z0)) → top(proper(z0))
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top(ok(z0)) → top(active(z0))
Tuples:
S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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FROM(ok(z0)) → c40(FROM(z0))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
S tuples:none
K tuples:
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
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POSRECIP(ok(z0)) → c31(POSRECIP(z0))
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PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
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PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
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PI(mark(z0)) → c47(PI(z0))
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PI(ok(z0)) → c48(PI(z0))
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PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
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2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
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FROM(ok(z0)) → c40(FROM(z0))
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RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
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RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
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FROM(mark(z0)) → c39(FROM(z0))
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TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
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TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
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SQUARE(mark(z0)) → c55(SQUARE(z0))
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SQUARE(ok(z0)) → c56(SQUARE(z0))
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NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
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NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
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RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
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2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
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2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
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2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
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2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
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2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
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S(mark(z0)) → c28(S(z0))
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S(ok(z0)) → c29(S(z0))
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CONS(mark(z0), z1) → c34(CONS(z0, z1))
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CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
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TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56
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(113) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
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(114) BOUNDS(O(1), O(1))
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