246.49/77.53
246.49/77.53
(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(from(X)) → mark(cons(X, from(s(X))))
246.49/77.53
active(sel(0, cons(X, XS))) → mark(X)
246.49/77.53
active(sel(s(N), cons(X, XS))) → mark(sel(N, XS))
246.49/77.53
active(minus(X, 0)) → mark(0)
246.49/77.53
active(minus(s(X), s(Y))) → mark(minus(X, Y))
246.49/77.53
active(quot(0, s(Y))) → mark(0)
246.49/77.53
active(quot(s(X), s(Y))) → mark(s(quot(minus(X, Y), s(Y))))
246.49/77.53
active(zWquot(XS, nil)) → mark(nil)
246.49/77.53
active(zWquot(nil, XS)) → mark(nil)
246.49/77.53
active(zWquot(cons(X, XS), cons(Y, YS))) → mark(cons(quot(X, Y), zWquot(XS, YS)))
246.49/77.53
active(from(X)) → from(active(X))
246.49/77.53
active(cons(X1, X2)) → cons(active(X1), X2)
246.49/77.53
active(s(X)) → s(active(X))
246.49/77.53
active(sel(X1, X2)) → sel(active(X1), X2)
246.49/77.53
active(sel(X1, X2)) → sel(X1, active(X2))
246.49/77.53
active(minus(X1, X2)) → minus(active(X1), X2)
246.49/77.53
active(minus(X1, X2)) → minus(X1, active(X2))
246.49/77.53
active(quot(X1, X2)) → quot(active(X1), X2)
246.49/77.53
active(quot(X1, X2)) → quot(X1, active(X2))
246.49/77.53
active(zWquot(X1, X2)) → zWquot(active(X1), X2)
246.49/77.53
active(zWquot(X1, X2)) → zWquot(X1, active(X2))
246.49/77.53
from(mark(X)) → mark(from(X))
246.49/77.53
cons(mark(X1), X2) → mark(cons(X1, X2))
246.49/77.53
s(mark(X)) → mark(s(X))
246.49/77.53
sel(mark(X1), X2) → mark(sel(X1, X2))
246.49/77.53
sel(X1, mark(X2)) → mark(sel(X1, X2))
246.49/77.53
minus(mark(X1), X2) → mark(minus(X1, X2))
246.49/77.53
minus(X1, mark(X2)) → mark(minus(X1, X2))
246.49/77.53
quot(mark(X1), X2) → mark(quot(X1, X2))
246.49/77.53
quot(X1, mark(X2)) → mark(quot(X1, X2))
246.49/77.53
zWquot(mark(X1), X2) → mark(zWquot(X1, X2))
246.49/77.53
zWquot(X1, mark(X2)) → mark(zWquot(X1, X2))
246.49/77.53
proper(from(X)) → from(proper(X))
246.49/77.53
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
246.49/77.53
proper(s(X)) → s(proper(X))
246.49/77.53
proper(sel(X1, X2)) → sel(proper(X1), proper(X2))
246.49/77.53
proper(0) → ok(0)
246.49/77.53
proper(minus(X1, X2)) → minus(proper(X1), proper(X2))
246.49/77.53
proper(quot(X1, X2)) → quot(proper(X1), proper(X2))
246.49/77.53
proper(zWquot(X1, X2)) → zWquot(proper(X1), proper(X2))
246.49/77.53
proper(nil) → ok(nil)
246.49/77.53
from(ok(X)) → ok(from(X))
246.49/77.53
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
246.49/77.53
s(ok(X)) → ok(s(X))
246.49/77.53
sel(ok(X1), ok(X2)) → ok(sel(X1, X2))
246.49/77.53
minus(ok(X1), ok(X2)) → ok(minus(X1, X2))
246.49/77.53
quot(ok(X1), ok(X2)) → ok(quot(X1, X2))
246.49/77.53
zWquot(ok(X1), ok(X2)) → ok(zWquot(X1, X2))
246.49/77.53
top(mark(X)) → top(proper(X))
246.49/77.53
top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
246.49/77.53
246.49/77.53
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted CpxTRS to CDT
246.49/77.53
246.49/77.53
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
246.49/77.53
active(sel(0, cons(z0, z1))) → mark(z0)
246.49/77.53
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
246.49/77.53
active(minus(z0, 0)) → mark(0)
246.49/77.53
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
246.49/77.53
active(quot(0, s(z0))) → mark(0)
246.49/77.53
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
246.49/77.53
active(zWquot(z0, nil)) → mark(nil)
246.49/77.53
active(zWquot(nil, z0)) → mark(nil)
246.49/77.53
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
246.49/77.53
active(from(z0)) → from(active(z0))
246.49/77.53
active(cons(z0, z1)) → cons(active(z0), z1)
246.49/77.53
active(s(z0)) → s(active(z0))
246.49/77.53
active(sel(z0, z1)) → sel(active(z0), z1)
246.49/77.53
active(sel(z0, z1)) → sel(z0, active(z1))
246.49/77.53
active(minus(z0, z1)) → minus(active(z0), z1)
246.49/77.53
active(minus(z0, z1)) → minus(z0, active(z1))
246.49/77.53
active(quot(z0, z1)) → quot(active(z0), z1)
246.49/77.53
active(quot(z0, z1)) → quot(z0, active(z1))
246.49/77.53
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
246.49/77.53
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
246.49/77.53
from(mark(z0)) → mark(from(z0))
246.49/77.53
from(ok(z0)) → ok(from(z0))
246.49/77.53
cons(mark(z0), z1) → mark(cons(z0, z1))
246.49/77.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
246.49/77.53
s(mark(z0)) → mark(s(z0))
246.49/77.53
s(ok(z0)) → ok(s(z0))
246.49/77.53
sel(mark(z0), z1) → mark(sel(z0, z1))
246.49/77.53
sel(z0, mark(z1)) → mark(sel(z0, z1))
246.49/77.53
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
246.49/77.53
minus(mark(z0), z1) → mark(minus(z0, z1))
246.49/77.53
minus(z0, mark(z1)) → mark(minus(z0, z1))
246.49/77.53
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
246.49/77.53
quot(mark(z0), z1) → mark(quot(z0, z1))
246.49/77.53
quot(z0, mark(z1)) → mark(quot(z0, z1))
246.49/77.53
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
246.49/77.53
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
246.49/77.53
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
246.49/77.53
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
246.49/77.53
proper(from(z0)) → from(proper(z0))
246.49/77.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
246.49/77.53
proper(s(z0)) → s(proper(z0))
246.49/77.53
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
246.49/77.53
proper(0) → ok(0)
246.49/77.53
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
246.49/77.53
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
246.49/77.53
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
246.49/77.53
proper(nil) → ok(nil)
246.49/77.53
top(mark(z0)) → top(proper(z0))
246.49/77.53
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
246.49/77.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
246.49/77.53
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
246.49/77.53
ACTIVE(quot(s(z0), s(z1))) → c6(S(quot(minus(z0, z1), s(z1))), QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1), S(z1))
246.49/77.53
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c9(CONS(quot(z0, z2), zWquot(z1, z3)), QUOT(z0, z2), ZWQUOT(z1, z3))
246.49/77.53
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
246.49/77.53
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
246.49/77.53
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
246.49/77.53
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
246.49/77.53
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
246.49/77.53
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
246.49/77.53
FROM(mark(z0)) → c21(FROM(z0))
246.49/77.53
FROM(ok(z0)) → c22(FROM(z0))
246.49/77.53
CONS(mark(z0), z1) → c23(CONS(z0, z1))
246.49/77.53
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
246.49/77.53
S(mark(z0)) → c25(S(z0))
246.49/77.53
S(ok(z0)) → c26(S(z0))
246.49/77.53
SEL(mark(z0), z1) → c27(SEL(z0, z1))
246.49/77.53
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
246.49/77.53
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
246.49/77.53
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
246.49/77.53
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
246.49/77.53
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
246.49/77.53
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
246.49/77.53
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
246.49/77.53
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
246.49/77.53
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
246.49/77.53
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
246.49/77.53
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
246.49/77.53
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
246.49/77.53
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.49/77.53
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
246.49/77.53
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.49/77.53
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.49/77.53
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.49/77.53
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.49/77.53
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
246.49/77.53
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
246.49/77.53
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
246.49/77.53
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
246.49/77.53
ACTIVE(quot(s(z0), s(z1))) → c6(S(quot(minus(z0, z1), s(z1))), QUOT(minus(z0, z1), s(z1)), MINUS(z0, z1), S(z1))
246.49/77.53
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c9(CONS(quot(z0, z2), zWquot(z1, z3)), QUOT(z0, z2), ZWQUOT(z1, z3))
246.49/77.53
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
246.49/77.53
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
246.49/77.53
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
246.49/77.53
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
FROM(mark(z0)) → c21(FROM(z0))
246.76/77.64
FROM(ok(z0)) → c22(FROM(z0))
246.76/77.64
CONS(mark(z0), z1) → c23(CONS(z0, z1))
246.76/77.64
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
246.76/77.64
S(mark(z0)) → c25(S(z0))
246.76/77.64
S(ok(z0)) → c26(S(z0))
246.76/77.64
SEL(mark(z0), z1) → c27(SEL(z0, z1))
246.76/77.64
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
246.76/77.64
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
246.76/77.64
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
246.76/77.64
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
246.76/77.64
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
246.76/77.64
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
246.76/77.64
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
246.76/77.64
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
246.76/77.64
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
246.76/77.64
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
246.76/77.64
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
246.76/77.64
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
246.76/77.64
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
246.76/77.64
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
246.76/77.64
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c, c2, c4, c6, 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, c44, c45, c46, c48, c49
246.76/77.64
246.76/77.64
(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
246.76/77.64
246.76/77.64
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
246.76/77.64
active(sel(0, cons(z0, z1))) → mark(z0)
246.76/77.64
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
246.76/77.64
active(minus(z0, 0)) → mark(0)
246.76/77.64
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
246.76/77.64
active(quot(0, s(z0))) → mark(0)
246.76/77.64
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
246.76/77.64
active(zWquot(z0, nil)) → mark(nil)
246.76/77.64
active(zWquot(nil, z0)) → mark(nil)
246.76/77.64
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
246.76/77.64
active(from(z0)) → from(active(z0))
246.76/77.64
active(cons(z0, z1)) → cons(active(z0), z1)
246.76/77.64
active(s(z0)) → s(active(z0))
246.76/77.64
active(sel(z0, z1)) → sel(active(z0), z1)
246.76/77.64
active(sel(z0, z1)) → sel(z0, active(z1))
246.76/77.64
active(minus(z0, z1)) → minus(active(z0), z1)
246.76/77.64
active(minus(z0, z1)) → minus(z0, active(z1))
246.76/77.64
active(quot(z0, z1)) → quot(active(z0), z1)
246.76/77.64
active(quot(z0, z1)) → quot(z0, active(z1))
246.76/77.64
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
246.76/77.64
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
246.76/77.64
from(mark(z0)) → mark(from(z0))
246.76/77.64
from(ok(z0)) → ok(from(z0))
246.76/77.64
cons(mark(z0), z1) → mark(cons(z0, z1))
246.76/77.64
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
246.76/77.64
s(mark(z0)) → mark(s(z0))
246.76/77.64
s(ok(z0)) → ok(s(z0))
246.76/77.64
sel(mark(z0), z1) → mark(sel(z0, z1))
246.76/77.64
sel(z0, mark(z1)) → mark(sel(z0, z1))
246.76/77.64
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
246.76/77.64
minus(mark(z0), z1) → mark(minus(z0, z1))
246.76/77.64
minus(z0, mark(z1)) → mark(minus(z0, z1))
246.76/77.64
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
246.76/77.64
quot(mark(z0), z1) → mark(quot(z0, z1))
246.76/77.64
quot(z0, mark(z1)) → mark(quot(z0, z1))
246.76/77.64
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
246.76/77.64
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
246.76/77.64
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
246.76/77.64
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
246.76/77.64
proper(from(z0)) → from(proper(z0))
246.76/77.64
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
246.76/77.64
proper(s(z0)) → s(proper(z0))
246.76/77.64
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
246.76/77.64
proper(0) → ok(0)
246.76/77.64
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
246.76/77.64
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
246.76/77.64
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
246.76/77.64
proper(nil) → ok(nil)
246.76/77.64
top(mark(z0)) → top(proper(z0))
246.76/77.64
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
246.76/77.64
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
246.76/77.64
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c9(CONS(quot(z0, z2), zWquot(z1, z3)), QUOT(z0, z2), ZWQUOT(z1, z3))
246.76/77.64
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
246.76/77.64
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
246.76/77.64
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
FROM(mark(z0)) → c21(FROM(z0))
246.76/77.64
FROM(ok(z0)) → c22(FROM(z0))
246.76/77.64
CONS(mark(z0), z1) → c23(CONS(z0, z1))
246.76/77.64
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
246.76/77.64
S(mark(z0)) → c25(S(z0))
246.76/77.64
S(ok(z0)) → c26(S(z0))
246.76/77.64
SEL(mark(z0), z1) → c27(SEL(z0, z1))
246.76/77.64
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
246.76/77.64
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
246.76/77.64
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
246.76/77.64
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
246.76/77.64
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
246.76/77.64
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
246.76/77.64
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
246.76/77.64
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
246.76/77.64
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
246.76/77.64
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
246.76/77.64
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
246.76/77.64
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
246.76/77.64
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
246.76/77.64
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
246.76/77.64
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
246.76/77.64
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
246.76/77.64
ACTIVE(from(z0)) → c(S(z0))
246.76/77.64
ACTIVE(quot(s(z0), s(z1))) → c6(MINUS(z0, z1), S(z1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
246.76/77.64
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
246.76/77.64
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c9(CONS(quot(z0, z2), zWquot(z1, z3)), QUOT(z0, z2), ZWQUOT(z1, z3))
246.76/77.64
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
246.76/77.64
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
246.76/77.64
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
246.76/77.64
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
246.76/77.64
FROM(mark(z0)) → c21(FROM(z0))
247.18/77.79
FROM(ok(z0)) → c22(FROM(z0))
247.18/77.79
CONS(mark(z0), z1) → c23(CONS(z0, z1))
247.18/77.79
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
247.18/77.79
S(mark(z0)) → c25(S(z0))
247.18/77.79
S(ok(z0)) → c26(S(z0))
247.18/77.79
SEL(mark(z0), z1) → c27(SEL(z0, z1))
247.18/77.79
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
247.18/77.79
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
247.18/77.79
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
247.18/77.79
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
247.18/77.79
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
247.18/77.79
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
247.18/77.79
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
247.18/77.79
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
247.18/77.79
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
247.18/77.79
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
247.18/77.79
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(from(z0)) → c(S(z0))
247.18/77.79
ACTIVE(quot(s(z0), s(z1))) → c6(MINUS(z0, z1), S(z1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c6
247.18/77.79
247.18/77.79
(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
247.18/77.79
247.18/77.79
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
247.18/77.79
active(sel(0, cons(z0, z1))) → mark(z0)
247.18/77.79
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
247.18/77.79
active(minus(z0, 0)) → mark(0)
247.18/77.79
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
247.18/77.79
active(quot(0, s(z0))) → mark(0)
247.18/77.79
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
247.18/77.79
active(zWquot(z0, nil)) → mark(nil)
247.18/77.79
active(zWquot(nil, z0)) → mark(nil)
247.18/77.79
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
247.18/77.79
active(from(z0)) → from(active(z0))
247.18/77.79
active(cons(z0, z1)) → cons(active(z0), z1)
247.18/77.79
active(s(z0)) → s(active(z0))
247.18/77.79
active(sel(z0, z1)) → sel(active(z0), z1)
247.18/77.79
active(sel(z0, z1)) → sel(z0, active(z1))
247.18/77.79
active(minus(z0, z1)) → minus(active(z0), z1)
247.18/77.79
active(minus(z0, z1)) → minus(z0, active(z1))
247.18/77.79
active(quot(z0, z1)) → quot(active(z0), z1)
247.18/77.79
active(quot(z0, z1)) → quot(z0, active(z1))
247.18/77.79
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
247.18/77.79
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
247.18/77.79
from(mark(z0)) → mark(from(z0))
247.18/77.79
from(ok(z0)) → ok(from(z0))
247.18/77.79
cons(mark(z0), z1) → mark(cons(z0, z1))
247.18/77.79
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
247.18/77.79
s(mark(z0)) → mark(s(z0))
247.18/77.79
s(ok(z0)) → ok(s(z0))
247.18/77.79
sel(mark(z0), z1) → mark(sel(z0, z1))
247.18/77.79
sel(z0, mark(z1)) → mark(sel(z0, z1))
247.18/77.79
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
247.18/77.79
minus(mark(z0), z1) → mark(minus(z0, z1))
247.18/77.79
minus(z0, mark(z1)) → mark(minus(z0, z1))
247.18/77.79
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
247.18/77.79
quot(mark(z0), z1) → mark(quot(z0, z1))
247.18/77.79
quot(z0, mark(z1)) → mark(quot(z0, z1))
247.18/77.79
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
247.18/77.79
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
247.18/77.79
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
247.18/77.79
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
247.18/77.79
proper(from(z0)) → from(proper(z0))
247.18/77.79
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
247.18/77.79
proper(s(z0)) → s(proper(z0))
247.18/77.79
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
247.18/77.79
proper(0) → ok(0)
247.18/77.79
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
247.18/77.79
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
247.18/77.79
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
247.18/77.79
proper(nil) → ok(nil)
247.18/77.79
top(mark(z0)) → top(proper(z0))
247.18/77.79
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
247.18/77.79
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
247.18/77.79
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
247.18/77.79
FROM(mark(z0)) → c21(FROM(z0))
247.18/77.79
FROM(ok(z0)) → c22(FROM(z0))
247.18/77.79
CONS(mark(z0), z1) → c23(CONS(z0, z1))
247.18/77.79
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
247.18/77.79
S(mark(z0)) → c25(S(z0))
247.18/77.79
S(ok(z0)) → c26(S(z0))
247.18/77.79
SEL(mark(z0), z1) → c27(SEL(z0, z1))
247.18/77.79
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
247.18/77.79
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
247.18/77.79
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
247.18/77.79
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
247.18/77.79
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
247.18/77.79
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
247.18/77.79
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
247.18/77.79
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
247.18/77.79
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
247.18/77.79
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
247.18/77.79
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(from(z0)) → c(S(z0))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
247.18/77.79
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
247.18/77.79
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
247.18/77.79
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
247.18/77.79
ACTIVE(from(z0)) → c10(FROM(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
247.18/77.79
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
247.18/77.79
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
247.18/77.79
FROM(mark(z0)) → c21(FROM(z0))
247.18/77.79
FROM(ok(z0)) → c22(FROM(z0))
247.18/77.79
CONS(mark(z0), z1) → c23(CONS(z0, z1))
247.18/77.79
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
247.18/77.79
S(mark(z0)) → c25(S(z0))
247.18/77.79
S(ok(z0)) → c26(S(z0))
247.18/77.79
SEL(mark(z0), z1) → c27(SEL(z0, z1))
247.18/77.79
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
247.18/77.79
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
247.18/77.79
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
247.18/77.79
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
247.18/77.79
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
247.18/77.79
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
247.18/77.79
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
247.18/77.79
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
247.18/77.79
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
247.18/77.79
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
247.18/77.79
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
247.18/77.79
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.18/77.79
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
247.18/77.79
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
247.18/77.79
ACTIVE(from(z0)) → c(S(z0))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
247.18/77.79
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
247.18/77.79
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
247.18/77.79
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, 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, c44, c45, c46, c48, c49, c, c1
247.18/77.79
247.18/77.79
(7) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
from(
z0)) →
c10(
FROM(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
247.18/77.79
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
247.18/77.79
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
247.18/77.79
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
247.18/77.79
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
247.18/77.79
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
247.18/77.79
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
247.18/77.79
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
247.18/77.79
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
247.18/77.79
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
247.18/77.79
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
247.18/77.79
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
247.18/77.79
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
247.18/77.79
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
247.18/77.79
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
247.18/77.79
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
247.18/77.79
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
247.18/77.79
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
247.18/77.79
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
247.18/77.79
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
247.18/77.79
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
247.18/77.79
247.18/77.79
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
247.18/77.79
active(sel(0, cons(z0, z1))) → mark(z0)
247.18/77.79
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
247.18/77.79
active(minus(z0, 0)) → mark(0)
247.18/77.79
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
247.57/77.86
active(quot(0, s(z0))) → mark(0)
247.57/77.86
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
247.57/77.86
active(zWquot(z0, nil)) → mark(nil)
247.57/77.86
active(zWquot(nil, z0)) → mark(nil)
247.57/77.86
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
247.57/77.86
active(from(z0)) → from(active(z0))
247.57/77.86
active(cons(z0, z1)) → cons(active(z0), z1)
247.57/77.86
active(s(z0)) → s(active(z0))
247.57/77.86
active(sel(z0, z1)) → sel(active(z0), z1)
247.57/77.86
active(sel(z0, z1)) → sel(z0, active(z1))
247.57/77.86
active(minus(z0, z1)) → minus(active(z0), z1)
247.57/77.86
active(minus(z0, z1)) → minus(z0, active(z1))
247.57/77.86
active(quot(z0, z1)) → quot(active(z0), z1)
247.57/77.86
active(quot(z0, z1)) → quot(z0, active(z1))
247.57/77.86
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
247.57/77.86
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
247.57/77.86
from(mark(z0)) → mark(from(z0))
247.57/77.86
from(ok(z0)) → ok(from(z0))
247.57/77.86
cons(mark(z0), z1) → mark(cons(z0, z1))
247.57/77.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
247.57/77.86
s(mark(z0)) → mark(s(z0))
247.57/77.86
s(ok(z0)) → ok(s(z0))
247.57/77.86
sel(mark(z0), z1) → mark(sel(z0, z1))
247.57/77.86
sel(z0, mark(z1)) → mark(sel(z0, z1))
247.57/77.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
247.57/77.86
minus(mark(z0), z1) → mark(minus(z0, z1))
247.57/77.86
minus(z0, mark(z1)) → mark(minus(z0, z1))
247.57/77.86
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
247.57/77.86
quot(mark(z0), z1) → mark(quot(z0, z1))
247.57/77.86
quot(z0, mark(z1)) → mark(quot(z0, z1))
247.57/77.86
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
247.57/77.86
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
247.57/77.86
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
247.57/77.86
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
247.57/77.86
proper(from(z0)) → from(proper(z0))
247.57/77.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
247.57/77.86
proper(s(z0)) → s(proper(z0))
247.57/77.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
247.57/77.86
proper(0) → ok(0)
247.57/77.86
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
247.57/77.86
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
247.57/77.86
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
247.57/77.86
proper(nil) → ok(nil)
247.57/77.86
top(mark(z0)) → top(proper(z0))
247.57/77.86
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
247.57/77.86
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
247.57/77.86
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
247.57/77.86
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
247.57/77.86
FROM(mark(z0)) → c21(FROM(z0))
247.57/77.86
FROM(ok(z0)) → c22(FROM(z0))
247.57/77.86
CONS(mark(z0), z1) → c23(CONS(z0, z1))
247.57/77.86
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
247.57/77.86
S(mark(z0)) → c25(S(z0))
247.57/77.86
S(ok(z0)) → c26(S(z0))
247.57/77.86
SEL(mark(z0), z1) → c27(SEL(z0, z1))
247.57/77.86
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
247.57/77.86
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
247.57/77.86
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
247.57/77.86
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
247.57/77.86
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
247.57/77.86
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
247.57/77.86
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
247.57/77.86
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
247.57/77.86
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
247.57/77.86
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
247.57/77.86
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
247.57/77.86
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
247.57/77.86
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
247.57/77.86
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
247.57/77.86
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
247.57/77.86
ACTIVE(from(z0)) → c(S(z0))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
247.57/77.86
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
247.57/77.86
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
247.57/77.86
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
247.57/77.86
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
247.57/77.86
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
247.57/77.86
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
247.57/77.86
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
247.57/77.86
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
247.57/77.86
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
247.57/77.86
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
247.57/77.86
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
247.57/77.86
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
247.57/77.86
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
247.57/77.86
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
247.57/77.86
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
247.57/77.86
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
247.57/77.86
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
247.57/77.86
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
247.57/77.86
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
247.57/77.86
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
247.57/77.86
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
247.57/77.86
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
247.57/77.86
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
247.57/77.86
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
247.57/77.86
ACTIVE(cons(z0, z1)) → c11(CONS(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
247.57/77.86
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
247.57/77.86
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
247.57/77.86
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
247.57/77.86
FROM(mark(z0)) → c21(FROM(z0))
247.57/77.86
FROM(ok(z0)) → c22(FROM(z0))
247.57/77.86
CONS(mark(z0), z1) → c23(CONS(z0, z1))
247.57/77.86
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
247.57/77.86
S(mark(z0)) → c25(S(z0))
247.57/77.86
S(ok(z0)) → c26(S(z0))
247.57/77.86
SEL(mark(z0), z1) → c27(SEL(z0, z1))
247.57/77.86
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
247.57/77.86
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
247.57/77.86
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
247.57/77.86
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
247.57/77.86
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
247.57/77.86
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
247.57/77.86
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
247.57/77.86
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
247.57/77.86
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
247.57/77.86
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
247.57/77.86
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
247.57/77.86
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
247.57/77.86
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
247.57/77.86
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
247.57/77.86
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
247.57/77.86
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
247.57/77.86
ACTIVE(from(z0)) → c(S(z0))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
247.57/77.86
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
247.57/77.86
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
247.57/77.86
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
247.57/77.86
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
247.57/77.86
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
247.57/77.86
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
247.57/77.86
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
247.57/77.86
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
247.57/77.86
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
247.57/77.86
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
247.57/77.86
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
247.57/77.86
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
247.57/77.86
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
247.57/77.86
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
247.57/77.86
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
247.57/77.86
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
247.57/77.86
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
247.57/77.86
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
247.57/77.86
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
247.57/77.86
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
247.57/77.86
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
247.57/77.86
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
247.57/77.86
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
247.57/77.86
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c1, c10
247.57/77.86
247.57/77.86
(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
cons(
z0,
z1)) →
c11(
CONS(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
247.57/77.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
247.57/77.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
247.57/77.87
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
247.57/77.87
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
247.57/77.87
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
248.77/78.12
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
248.77/78.12
active(sel(0, cons(z0, z1))) → mark(z0)
248.77/78.12
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
248.77/78.12
active(minus(z0, 0)) → mark(0)
248.77/78.12
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
248.77/78.12
active(quot(0, s(z0))) → mark(0)
248.77/78.12
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
248.77/78.12
active(zWquot(z0, nil)) → mark(nil)
248.77/78.12
active(zWquot(nil, z0)) → mark(nil)
248.77/78.12
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
248.77/78.12
active(from(z0)) → from(active(z0))
248.77/78.12
active(cons(z0, z1)) → cons(active(z0), z1)
248.77/78.12
active(s(z0)) → s(active(z0))
248.77/78.12
active(sel(z0, z1)) → sel(active(z0), z1)
248.77/78.12
active(sel(z0, z1)) → sel(z0, active(z1))
248.77/78.12
active(minus(z0, z1)) → minus(active(z0), z1)
248.77/78.12
active(minus(z0, z1)) → minus(z0, active(z1))
248.77/78.12
active(quot(z0, z1)) → quot(active(z0), z1)
248.77/78.12
active(quot(z0, z1)) → quot(z0, active(z1))
248.77/78.12
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
248.77/78.12
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
248.77/78.12
from(mark(z0)) → mark(from(z0))
248.77/78.12
from(ok(z0)) → ok(from(z0))
248.77/78.12
cons(mark(z0), z1) → mark(cons(z0, z1))
248.77/78.12
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
248.77/78.12
s(mark(z0)) → mark(s(z0))
248.77/78.12
s(ok(z0)) → ok(s(z0))
248.77/78.12
sel(mark(z0), z1) → mark(sel(z0, z1))
248.77/78.12
sel(z0, mark(z1)) → mark(sel(z0, z1))
248.77/78.12
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
248.77/78.12
minus(mark(z0), z1) → mark(minus(z0, z1))
248.77/78.12
minus(z0, mark(z1)) → mark(minus(z0, z1))
248.77/78.12
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
248.77/78.12
quot(mark(z0), z1) → mark(quot(z0, z1))
248.77/78.12
quot(z0, mark(z1)) → mark(quot(z0, z1))
248.77/78.12
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
248.77/78.12
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
248.77/78.12
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
248.77/78.12
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
248.77/78.12
proper(from(z0)) → from(proper(z0))
248.77/78.12
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
248.77/78.12
proper(s(z0)) → s(proper(z0))
248.77/78.12
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
248.77/78.12
proper(0) → ok(0)
248.77/78.12
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
248.77/78.12
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
248.77/78.12
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
248.77/78.12
proper(nil) → ok(nil)
248.77/78.12
top(mark(z0)) → top(proper(z0))
248.77/78.12
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
248.77/78.12
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
248.77/78.12
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
FROM(mark(z0)) → c21(FROM(z0))
248.77/78.12
FROM(ok(z0)) → c22(FROM(z0))
248.77/78.12
CONS(mark(z0), z1) → c23(CONS(z0, z1))
248.77/78.12
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
248.77/78.12
S(mark(z0)) → c25(S(z0))
248.77/78.12
S(ok(z0)) → c26(S(z0))
248.77/78.12
SEL(mark(z0), z1) → c27(SEL(z0, z1))
248.77/78.12
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
248.77/78.12
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
248.77/78.12
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
248.77/78.12
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
248.77/78.12
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
248.77/78.12
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
248.77/78.12
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
248.77/78.12
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
248.77/78.12
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
248.77/78.12
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
248.77/78.12
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(from(z0)) → c(S(z0))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
248.77/78.12
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
248.77/78.12
ACTIVE(s(z0)) → c12(S(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
FROM(mark(z0)) → c21(FROM(z0))
248.77/78.12
FROM(ok(z0)) → c22(FROM(z0))
248.77/78.12
CONS(mark(z0), z1) → c23(CONS(z0, z1))
248.77/78.12
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
248.77/78.12
S(mark(z0)) → c25(S(z0))
248.77/78.12
S(ok(z0)) → c26(S(z0))
248.77/78.12
SEL(mark(z0), z1) → c27(SEL(z0, z1))
248.77/78.12
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
248.77/78.12
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
248.77/78.12
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
248.77/78.12
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
248.77/78.12
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
248.77/78.12
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
248.77/78.12
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
248.77/78.12
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
248.77/78.12
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
248.77/78.12
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
248.77/78.12
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(from(z0)) → c(S(z0))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c1, c10, c11
248.77/78.12
248.77/78.12
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s(
z0)) →
c12(
S(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
248.77/78.12
248.77/78.12
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
248.77/78.12
active(sel(0, cons(z0, z1))) → mark(z0)
248.77/78.12
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
248.77/78.12
active(minus(z0, 0)) → mark(0)
248.77/78.12
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
248.77/78.12
active(quot(0, s(z0))) → mark(0)
248.77/78.12
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
248.77/78.12
active(zWquot(z0, nil)) → mark(nil)
248.77/78.12
active(zWquot(nil, z0)) → mark(nil)
248.77/78.12
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
248.77/78.12
active(from(z0)) → from(active(z0))
248.77/78.12
active(cons(z0, z1)) → cons(active(z0), z1)
248.77/78.12
active(s(z0)) → s(active(z0))
248.77/78.12
active(sel(z0, z1)) → sel(active(z0), z1)
248.77/78.12
active(sel(z0, z1)) → sel(z0, active(z1))
248.77/78.12
active(minus(z0, z1)) → minus(active(z0), z1)
248.77/78.12
active(minus(z0, z1)) → minus(z0, active(z1))
248.77/78.12
active(quot(z0, z1)) → quot(active(z0), z1)
248.77/78.12
active(quot(z0, z1)) → quot(z0, active(z1))
248.77/78.12
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
248.77/78.12
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
248.77/78.12
from(mark(z0)) → mark(from(z0))
248.77/78.12
from(ok(z0)) → ok(from(z0))
248.77/78.12
cons(mark(z0), z1) → mark(cons(z0, z1))
248.77/78.12
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
248.77/78.12
s(mark(z0)) → mark(s(z0))
248.77/78.12
s(ok(z0)) → ok(s(z0))
248.77/78.12
sel(mark(z0), z1) → mark(sel(z0, z1))
248.77/78.12
sel(z0, mark(z1)) → mark(sel(z0, z1))
248.77/78.12
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
248.77/78.12
minus(mark(z0), z1) → mark(minus(z0, z1))
248.77/78.12
minus(z0, mark(z1)) → mark(minus(z0, z1))
248.77/78.12
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
248.77/78.12
quot(mark(z0), z1) → mark(quot(z0, z1))
248.77/78.12
quot(z0, mark(z1)) → mark(quot(z0, z1))
248.77/78.12
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
248.77/78.12
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
248.77/78.12
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
248.77/78.12
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
248.77/78.12
proper(from(z0)) → from(proper(z0))
248.77/78.12
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
248.77/78.12
proper(s(z0)) → s(proper(z0))
248.77/78.12
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
248.77/78.12
proper(0) → ok(0)
248.77/78.12
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
248.77/78.12
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
248.77/78.12
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
248.77/78.12
proper(nil) → ok(nil)
248.77/78.12
top(mark(z0)) → top(proper(z0))
248.77/78.12
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
248.77/78.12
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
248.77/78.12
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
FROM(mark(z0)) → c21(FROM(z0))
248.77/78.12
FROM(ok(z0)) → c22(FROM(z0))
248.77/78.12
CONS(mark(z0), z1) → c23(CONS(z0, z1))
248.77/78.12
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
248.77/78.12
S(mark(z0)) → c25(S(z0))
248.77/78.12
S(ok(z0)) → c26(S(z0))
248.77/78.12
SEL(mark(z0), z1) → c27(SEL(z0, z1))
248.77/78.12
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
248.77/78.12
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
248.77/78.12
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
248.77/78.12
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
248.77/78.12
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
248.77/78.12
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
248.77/78.12
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
248.77/78.12
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
248.77/78.12
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
248.77/78.12
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
248.77/78.12
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(from(z0)) → c(S(z0))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
248.77/78.12
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
248.77/78.12
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.12
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.12
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.12
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.12
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.12
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.12
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.12
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.12
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.12
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
248.77/78.12
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.12
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
248.77/78.12
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.12
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.12
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.12
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.12
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
248.77/78.12
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
248.77/78.12
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
248.77/78.12
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
248.77/78.12
FROM(mark(z0)) → c21(FROM(z0))
248.77/78.12
FROM(ok(z0)) → c22(FROM(z0))
248.77/78.12
CONS(mark(z0), z1) → c23(CONS(z0, z1))
248.77/78.12
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
248.77/78.12
S(mark(z0)) → c25(S(z0))
248.77/78.12
S(ok(z0)) → c26(S(z0))
248.77/78.12
SEL(mark(z0), z1) → c27(SEL(z0, z1))
248.77/78.12
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
248.77/78.12
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
248.77/78.12
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
248.77/78.12
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
248.77/78.12
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
248.77/78.12
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
248.77/78.12
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
248.77/78.12
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
248.77/78.12
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
248.77/78.12
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
248.77/78.12
PROPER(from(z0)) → c39(FROM(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
248.77/78.12
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
248.77/78.12
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
248.77/78.12
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
248.77/78.12
ACTIVE(from(z0)) → c(S(z0))
248.77/78.13
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
248.77/78.13
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
248.77/78.13
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
248.77/78.13
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
248.77/78.13
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
248.77/78.13
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.13
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.13
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.13
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.13
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.13
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.13
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.13
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.13
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.13
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.13
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
248.77/78.13
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
248.77/78.13
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
248.77/78.13
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
248.77/78.13
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
248.77/78.13
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
248.77/78.13
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
248.77/78.13
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
248.77/78.13
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
248.77/78.13
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
248.77/78.13
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
248.77/78.13
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
248.77/78.13
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.13
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.13
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
248.77/78.13
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
248.77/78.13
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
248.77/78.13
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
248.77/78.13
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
248.77/78.13
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
248.77/78.13
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
248.77/78.13
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
248.77/78.13
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
248.77/78.13
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
248.77/78.13
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
248.77/78.13
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
248.77/78.13
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
248.77/78.13
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
248.77/78.13
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
248.77/78.13
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
248.77/78.13
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.13
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
248.77/78.13
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
248.77/78.13
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
248.77/78.13
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
248.77/78.13
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
248.77/78.13
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
248.77/78.13
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
248.77/78.13
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
248.77/78.13
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
248.77/78.13
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
248.77/78.13
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c1, c10, c11, c12
249.92/78.42
249.92/78.42
(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
from(
z0)) →
c39(
FROM(
proper(
z0)),
PROPER(
z0)) by
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.42
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.42
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.42
PROPER(from(0)) → c39(FROM(ok(0)), PROPER(0))
249.92/78.42
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.42
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.42
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.42
PROPER(from(nil)) → c39(FROM(ok(nil)), PROPER(nil))
249.92/78.42
249.92/78.42
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.42
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.42
active(minus(z0, 0)) → mark(0)
249.92/78.42
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.42
active(quot(0, s(z0))) → mark(0)
249.92/78.42
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.42
active(zWquot(z0, nil)) → mark(nil)
249.92/78.42
active(zWquot(nil, z0)) → mark(nil)
249.92/78.42
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
active(from(z0)) → from(active(z0))
249.92/78.42
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.42
active(s(z0)) → s(active(z0))
249.92/78.42
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.42
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.42
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.42
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.42
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.42
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.42
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.42
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.42
from(mark(z0)) → mark(from(z0))
249.92/78.42
from(ok(z0)) → ok(from(z0))
249.92/78.42
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.42
s(mark(z0)) → mark(s(z0))
249.92/78.42
s(ok(z0)) → ok(s(z0))
249.92/78.42
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.42
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.42
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.42
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.42
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.42
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.42
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.42
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.42
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.42
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.42
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.42
proper(from(z0)) → from(proper(z0))
249.92/78.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.42
proper(s(z0)) → s(proper(z0))
249.92/78.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.42
proper(0) → ok(0)
249.92/78.42
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.42
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.42
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.42
proper(nil) → ok(nil)
249.92/78.42
top(mark(z0)) → top(proper(z0))
249.92/78.42
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.42
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.42
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.42
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.42
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.42
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.42
S(mark(z0)) → c25(S(z0))
249.92/78.42
S(ok(z0)) → c26(S(z0))
249.92/78.42
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.42
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.42
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.42
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.42
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.42
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.42
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.42
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.42
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.42
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.42
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.42
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.42
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.42
ACTIVE(from(z0)) → c(S(z0))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.42
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.42
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.42
PROPER(from(0)) → c39(FROM(ok(0)), PROPER(0))
249.92/78.42
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.42
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.42
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.42
PROPER(from(nil)) → c39(FROM(ok(nil)), PROPER(nil))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.42
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.42
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.42
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.42
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.42
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.42
S(mark(z0)) → c25(S(z0))
249.92/78.42
S(ok(z0)) → c26(S(z0))
249.92/78.42
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.42
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.42
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.42
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.42
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.42
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.42
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.42
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.42
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.42
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.42
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.42
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.42
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.42
ACTIVE(from(z0)) → c(S(z0))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.42
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.42
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.42
PROPER(from(0)) → c39(FROM(ok(0)), PROPER(0))
249.92/78.42
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.42
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.42
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.42
PROPER(from(nil)) → c39(FROM(ok(nil)), PROPER(nil))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c40, c41, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39
249.92/78.42
249.92/78.42
(15) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
249.92/78.42
249.92/78.42
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.42
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.42
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.42
active(minus(z0, 0)) → mark(0)
249.92/78.42
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.42
active(quot(0, s(z0))) → mark(0)
249.92/78.42
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.42
active(zWquot(z0, nil)) → mark(nil)
249.92/78.42
active(zWquot(nil, z0)) → mark(nil)
249.92/78.42
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
active(from(z0)) → from(active(z0))
249.92/78.42
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.42
active(s(z0)) → s(active(z0))
249.92/78.42
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.42
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.42
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.42
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.42
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.42
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.42
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.42
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.42
from(mark(z0)) → mark(from(z0))
249.92/78.42
from(ok(z0)) → ok(from(z0))
249.92/78.42
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.42
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.42
s(mark(z0)) → mark(s(z0))
249.92/78.42
s(ok(z0)) → ok(s(z0))
249.92/78.42
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.42
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.42
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.42
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.42
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.42
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.42
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.42
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.42
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.42
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.42
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.42
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.42
proper(from(z0)) → from(proper(z0))
249.92/78.42
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.42
proper(s(z0)) → s(proper(z0))
249.92/78.42
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.42
proper(0) → ok(0)
249.92/78.42
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.42
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.42
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.42
proper(nil) → ok(nil)
249.92/78.42
top(mark(z0)) → top(proper(z0))
249.92/78.42
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.42
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.42
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.42
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.42
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.42
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.42
S(mark(z0)) → c25(S(z0))
249.92/78.42
S(ok(z0)) → c26(S(z0))
249.92/78.42
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.42
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.42
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.42
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.42
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.42
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.42
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.42
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.42
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.42
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.42
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.42
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.42
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.42
ACTIVE(from(z0)) → c(S(z0))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.42
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.42
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.42
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.42
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.42
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.42
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.42
PROPER(from(nil)) → c39(FROM(ok(nil)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.42
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.42
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.42
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.42
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.42
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.42
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.42
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.42
S(mark(z0)) → c25(S(z0))
249.92/78.42
S(ok(z0)) → c26(S(z0))
249.92/78.42
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.42
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.42
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.42
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.42
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.42
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.42
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.42
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.42
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.42
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.42
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.42
PROPER(cons(z0, z1)) → c40(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.42
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.42
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.42
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.42
ACTIVE(from(z0)) → c(S(z0))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.42
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.42
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.42
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.42
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.42
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.42
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.42
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.42
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.42
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.42
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.42
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.42
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.42
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.42
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.42
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.42
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.42
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.42
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.42
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.42
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.42
PROPER(from(nil)) → c39(FROM(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c40, c41, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39
249.92/78.42
249.92/78.42
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons(
z0,
z1)) →
c40(
CONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.42
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.42
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.42
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.44
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.44
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.44
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
249.92/78.44
249.92/78.44
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.44
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.44
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.44
active(minus(z0, 0)) → mark(0)
249.92/78.44
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.44
active(quot(0, s(z0))) → mark(0)
249.92/78.44
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.44
active(zWquot(z0, nil)) → mark(nil)
249.92/78.44
active(zWquot(nil, z0)) → mark(nil)
249.92/78.44
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
active(from(z0)) → from(active(z0))
249.92/78.44
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.44
active(s(z0)) → s(active(z0))
249.92/78.44
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.44
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.44
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.44
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.44
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.44
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.44
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.44
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.44
from(mark(z0)) → mark(from(z0))
249.92/78.44
from(ok(z0)) → ok(from(z0))
249.92/78.44
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.44
s(mark(z0)) → mark(s(z0))
249.92/78.44
s(ok(z0)) → ok(s(z0))
249.92/78.44
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.44
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.44
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.44
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.44
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.44
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.44
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.44
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.44
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.44
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.44
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.44
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.44
proper(from(z0)) → from(proper(z0))
249.92/78.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.44
proper(s(z0)) → s(proper(z0))
249.92/78.44
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.44
proper(0) → ok(0)
249.92/78.44
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.44
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.44
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.44
proper(nil) → ok(nil)
249.92/78.44
top(mark(z0)) → top(proper(z0))
249.92/78.44
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.44
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.44
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.44
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.44
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.44
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.44
S(mark(z0)) → c25(S(z0))
249.92/78.44
S(ok(z0)) → c26(S(z0))
249.92/78.44
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.44
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.44
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.44
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.44
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.44
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.44
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.44
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.44
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.44
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.44
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.44
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.44
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.44
ACTIVE(from(z0)) → c(S(z0))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.44
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.44
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.44
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.44
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.44
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.44
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.44
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.44
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.44
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.44
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.44
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.44
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.44
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.44
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.44
S(mark(z0)) → c25(S(z0))
249.92/78.44
S(ok(z0)) → c26(S(z0))
249.92/78.44
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.44
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.44
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.44
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.44
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.44
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.44
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.44
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.44
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.44
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.44
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.44
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.44
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.44
ACTIVE(from(z0)) → c(S(z0))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.44
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.44
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.44
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.44
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.44
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.44
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.44
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.44
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.44
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c41, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40
249.92/78.44
249.92/78.44
(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
249.92/78.44
249.92/78.44
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.44
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.44
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.44
active(minus(z0, 0)) → mark(0)
249.92/78.44
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.44
active(quot(0, s(z0))) → mark(0)
249.92/78.44
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.44
active(zWquot(z0, nil)) → mark(nil)
249.92/78.44
active(zWquot(nil, z0)) → mark(nil)
249.92/78.44
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
active(from(z0)) → from(active(z0))
249.92/78.44
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.44
active(s(z0)) → s(active(z0))
249.92/78.44
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.44
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.44
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.44
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.44
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.44
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.44
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.44
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.44
from(mark(z0)) → mark(from(z0))
249.92/78.44
from(ok(z0)) → ok(from(z0))
249.92/78.44
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.44
s(mark(z0)) → mark(s(z0))
249.92/78.44
s(ok(z0)) → ok(s(z0))
249.92/78.44
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.44
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.44
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.44
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.44
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.44
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.44
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.44
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.44
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.44
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.44
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.44
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.44
proper(from(z0)) → from(proper(z0))
249.92/78.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.44
proper(s(z0)) → s(proper(z0))
249.92/78.44
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.44
proper(0) → ok(0)
249.92/78.44
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.44
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.44
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.44
proper(nil) → ok(nil)
249.92/78.44
top(mark(z0)) → top(proper(z0))
249.92/78.44
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.44
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.44
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.44
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.44
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.44
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.44
S(mark(z0)) → c25(S(z0))
249.92/78.44
S(ok(z0)) → c26(S(z0))
249.92/78.44
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.44
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.44
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.44
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.44
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.44
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.44
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.44
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.44
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.44
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.44
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.44
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.44
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.44
ACTIVE(from(z0)) → c(S(z0))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.44
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.44
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.44
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.44
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.44
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.44
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.44
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.44
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.44
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.44
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.44
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.44
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.44
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.44
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.44
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.44
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.44
S(mark(z0)) → c25(S(z0))
249.92/78.44
S(ok(z0)) → c26(S(z0))
249.92/78.44
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.44
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.44
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.44
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.44
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.44
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.44
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.44
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.44
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.44
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.44
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.44
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0))
249.92/78.44
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.44
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.44
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.44
ACTIVE(from(z0)) → c(S(z0))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.44
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.44
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.44
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.44
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.44
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.44
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.44
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.44
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.44
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.44
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.44
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.44
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.44
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.44
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.44
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.44
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.44
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.44
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.44
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.44
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.44
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.44
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.44
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.44
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.44
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.44
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.44
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.46
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.46
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c41, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40
249.92/78.46
249.92/78.46
(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c41(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(s(0)) → c41(S(ok(0)), PROPER(0))
249.92/78.46
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))
249.92/78.46
249.92/78.46
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.46
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.46
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.46
active(minus(z0, 0)) → mark(0)
249.92/78.46
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.46
active(quot(0, s(z0))) → mark(0)
249.92/78.46
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.46
active(zWquot(z0, nil)) → mark(nil)
249.92/78.46
active(zWquot(nil, z0)) → mark(nil)
249.92/78.46
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
active(from(z0)) → from(active(z0))
249.92/78.46
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.46
active(s(z0)) → s(active(z0))
249.92/78.46
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.46
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.46
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.46
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.46
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.46
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.46
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.46
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.46
from(mark(z0)) → mark(from(z0))
249.92/78.46
from(ok(z0)) → ok(from(z0))
249.92/78.46
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.46
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.46
s(mark(z0)) → mark(s(z0))
249.92/78.46
s(ok(z0)) → ok(s(z0))
249.92/78.46
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.46
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.46
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.46
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.46
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.46
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.46
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.46
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.46
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.46
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.46
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.46
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.46
proper(from(z0)) → from(proper(z0))
249.92/78.46
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.46
proper(s(z0)) → s(proper(z0))
249.92/78.46
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.46
proper(0) → ok(0)
249.92/78.46
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.46
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.46
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.46
proper(nil) → ok(nil)
249.92/78.46
top(mark(z0)) → top(proper(z0))
249.92/78.46
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.46
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.46
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.46
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.46
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.46
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.46
S(mark(z0)) → c25(S(z0))
249.92/78.46
S(ok(z0)) → c26(S(z0))
249.92/78.46
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.46
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.46
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.46
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.46
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.46
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.46
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.46
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.46
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.46
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.46
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.46
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.46
ACTIVE(from(z0)) → c(S(z0))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.46
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.46
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.46
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.46
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.46
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.46
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(s(0)) → c41(S(ok(0)), PROPER(0))
249.92/78.46
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.46
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.46
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.46
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.46
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.46
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.46
S(mark(z0)) → c25(S(z0))
249.92/78.46
S(ok(z0)) → c26(S(z0))
249.92/78.46
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.46
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.46
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.46
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.46
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.46
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.46
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.46
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.46
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.46
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.46
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.46
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.46
ACTIVE(from(z0)) → c(S(z0))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.46
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.46
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.46
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.46
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.46
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.46
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(s(0)) → c41(S(ok(0)), PROPER(0))
249.92/78.46
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41
249.92/78.46
249.92/78.46
(23) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
249.92/78.46
249.92/78.46
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.46
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.46
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.46
active(minus(z0, 0)) → mark(0)
249.92/78.46
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.46
active(quot(0, s(z0))) → mark(0)
249.92/78.46
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.46
active(zWquot(z0, nil)) → mark(nil)
249.92/78.46
active(zWquot(nil, z0)) → mark(nil)
249.92/78.46
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
active(from(z0)) → from(active(z0))
249.92/78.46
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.46
active(s(z0)) → s(active(z0))
249.92/78.46
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.46
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.46
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.46
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.46
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.46
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.46
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.46
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.46
from(mark(z0)) → mark(from(z0))
249.92/78.46
from(ok(z0)) → ok(from(z0))
249.92/78.46
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.46
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.46
s(mark(z0)) → mark(s(z0))
249.92/78.46
s(ok(z0)) → ok(s(z0))
249.92/78.46
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.46
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.46
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.46
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.46
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.46
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.46
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.46
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.46
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.46
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.46
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.46
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.46
proper(from(z0)) → from(proper(z0))
249.92/78.46
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.46
proper(s(z0)) → s(proper(z0))
249.92/78.46
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.46
proper(0) → ok(0)
249.92/78.46
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.46
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.46
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.46
proper(nil) → ok(nil)
249.92/78.46
top(mark(z0)) → top(proper(z0))
249.92/78.46
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.46
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.46
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.46
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.46
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.46
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.46
S(mark(z0)) → c25(S(z0))
249.92/78.46
S(ok(z0)) → c26(S(z0))
249.92/78.46
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.46
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.46
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.46
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.46
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.46
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.46
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.46
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.46
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.46
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.46
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.46
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.46
ACTIVE(from(z0)) → c(S(z0))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.46
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.46
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.46
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.46
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.46
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.46
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.46
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.46
PROPER(s(nil)) → c41(S(ok(nil)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.46
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.46
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.46
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.46
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.46
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.46
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.46
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.46
S(mark(z0)) → c25(S(z0))
249.92/78.46
S(ok(z0)) → c26(S(z0))
249.92/78.46
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.46
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.46
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.46
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.46
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.46
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.46
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.46
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.46
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.46
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.46
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.46
PROPER(sel(z0, z1)) → c42(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.46
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.46
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.46
ACTIVE(from(z0)) → c(S(z0))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.46
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.46
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.46
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.46
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.46
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.46
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.46
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.46
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.46
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.46
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.46
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.46
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.46
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.46
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.46
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.46
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.46
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.46
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.46
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.46
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.46
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.46
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.46
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.46
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.46
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.46
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.46
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.47
PROPER(s(nil)) → c41(S(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c42, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41
249.92/78.47
249.92/78.47
(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
sel(
z0,
z1)) →
c42(
SEL(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.47
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.47
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.47
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
249.92/78.47
249.92/78.47
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.47
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.47
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.47
active(minus(z0, 0)) → mark(0)
249.92/78.47
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.47
active(quot(0, s(z0))) → mark(0)
249.92/78.47
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.47
active(zWquot(z0, nil)) → mark(nil)
249.92/78.47
active(zWquot(nil, z0)) → mark(nil)
249.92/78.47
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
active(from(z0)) → from(active(z0))
249.92/78.47
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.47
active(s(z0)) → s(active(z0))
249.92/78.47
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.47
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.47
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.47
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.47
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.47
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.47
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.47
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.47
from(mark(z0)) → mark(from(z0))
249.92/78.47
from(ok(z0)) → ok(from(z0))
249.92/78.47
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.47
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.47
s(mark(z0)) → mark(s(z0))
249.92/78.47
s(ok(z0)) → ok(s(z0))
249.92/78.47
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.47
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.47
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.47
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.47
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.47
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.47
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.47
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.47
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.47
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.47
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.47
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.47
proper(from(z0)) → from(proper(z0))
249.92/78.47
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.47
proper(s(z0)) → s(proper(z0))
249.92/78.47
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.47
proper(0) → ok(0)
249.92/78.47
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.47
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.47
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.47
proper(nil) → ok(nil)
249.92/78.47
top(mark(z0)) → top(proper(z0))
249.92/78.47
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.47
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.47
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.47
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.47
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.47
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.47
S(mark(z0)) → c25(S(z0))
249.92/78.47
S(ok(z0)) → c26(S(z0))
249.92/78.47
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.47
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.47
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.47
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.47
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.47
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.47
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.47
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.47
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.47
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.47
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.47
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.47
ACTIVE(from(z0)) → c(S(z0))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.47
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.47
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.47
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.47
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.47
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.47
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.47
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.47
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.47
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.47
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.47
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.47
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.47
S(mark(z0)) → c25(S(z0))
249.92/78.47
S(ok(z0)) → c26(S(z0))
249.92/78.47
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.47
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.47
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.47
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.47
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.47
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.47
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.47
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.47
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.47
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.47
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.47
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.47
ACTIVE(from(z0)) → c(S(z0))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.47
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.47
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.47
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.47
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.47
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.47
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.47
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42
249.92/78.47
249.92/78.47
(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
249.92/78.47
249.92/78.47
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.47
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.47
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.47
active(minus(z0, 0)) → mark(0)
249.92/78.47
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.47
active(quot(0, s(z0))) → mark(0)
249.92/78.47
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.47
active(zWquot(z0, nil)) → mark(nil)
249.92/78.47
active(zWquot(nil, z0)) → mark(nil)
249.92/78.47
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
active(from(z0)) → from(active(z0))
249.92/78.47
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.47
active(s(z0)) → s(active(z0))
249.92/78.47
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.47
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.47
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.47
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.47
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.47
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.47
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.47
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.47
from(mark(z0)) → mark(from(z0))
249.92/78.47
from(ok(z0)) → ok(from(z0))
249.92/78.47
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.47
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.47
s(mark(z0)) → mark(s(z0))
249.92/78.47
s(ok(z0)) → ok(s(z0))
249.92/78.47
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.47
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.47
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.47
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.47
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.47
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.47
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.47
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.47
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.47
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.47
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.47
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.47
proper(from(z0)) → from(proper(z0))
249.92/78.47
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.47
proper(s(z0)) → s(proper(z0))
249.92/78.47
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.47
proper(0) → ok(0)
249.92/78.47
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.47
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.47
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.47
proper(nil) → ok(nil)
249.92/78.47
top(mark(z0)) → top(proper(z0))
249.92/78.47
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.47
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.47
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.47
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.47
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.47
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.47
S(mark(z0)) → c25(S(z0))
249.92/78.47
S(ok(z0)) → c26(S(z0))
249.92/78.47
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.47
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.47
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.47
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.47
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.47
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.47
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.47
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.47
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.47
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.47
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.47
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.47
ACTIVE(from(z0)) → c(S(z0))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.47
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.47
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.47
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.47
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.47
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.47
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.47
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.47
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.47
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.47
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.47
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.47
S(mark(z0)) → c25(S(z0))
249.92/78.47
S(ok(z0)) → c26(S(z0))
249.92/78.47
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.47
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.47
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.47
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.47
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.47
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.47
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.47
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.47
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.47
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.47
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.47
PROPER(minus(z0, z1)) → c44(MINUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.47
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.47
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.47
ACTIVE(from(z0)) → c(S(z0))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.47
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.47
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.47
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.47
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.47
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.47
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.47
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.47
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.47
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.47
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.47
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.47
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.47
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.47
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.47
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.47
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.47
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.47
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.47
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.47
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.47
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.47
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.47
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.47
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.47
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.47
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.47
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.47
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.47
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c44, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42
249.92/78.47
249.92/78.47
(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
minus(
z0,
z1)) →
c44(
MINUS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.47
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.47
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.47
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.49
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.49
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.49
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
249.92/78.49
249.92/78.49
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.49
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.49
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.49
active(minus(z0, 0)) → mark(0)
249.92/78.49
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.49
active(quot(0, s(z0))) → mark(0)
249.92/78.49
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.49
active(zWquot(z0, nil)) → mark(nil)
249.92/78.49
active(zWquot(nil, z0)) → mark(nil)
249.92/78.49
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
active(from(z0)) → from(active(z0))
249.92/78.49
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.49
active(s(z0)) → s(active(z0))
249.92/78.49
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.49
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.49
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.49
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.49
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.49
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.49
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.49
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.49
from(mark(z0)) → mark(from(z0))
249.92/78.49
from(ok(z0)) → ok(from(z0))
249.92/78.49
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.49
s(mark(z0)) → mark(s(z0))
249.92/78.49
s(ok(z0)) → ok(s(z0))
249.92/78.49
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.49
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.49
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.49
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.49
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.49
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.49
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.49
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.49
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.49
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.49
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.49
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.49
proper(from(z0)) → from(proper(z0))
249.92/78.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.49
proper(s(z0)) → s(proper(z0))
249.92/78.49
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.49
proper(0) → ok(0)
249.92/78.49
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.49
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.49
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.49
proper(nil) → ok(nil)
249.92/78.49
top(mark(z0)) → top(proper(z0))
249.92/78.49
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.49
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.49
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.49
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.49
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.49
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.49
S(mark(z0)) → c25(S(z0))
249.92/78.49
S(ok(z0)) → c26(S(z0))
249.92/78.49
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.49
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.49
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.49
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.49
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.49
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.49
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.49
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.49
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.49
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.49
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.49
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.49
ACTIVE(from(z0)) → c(S(z0))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.49
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.49
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.49
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.49
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.49
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.49
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.49
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.49
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.49
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.49
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.49
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.49
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.49
S(mark(z0)) → c25(S(z0))
249.92/78.49
S(ok(z0)) → c26(S(z0))
249.92/78.49
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.49
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.49
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.49
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.49
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.49
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.49
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.49
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.49
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.49
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.49
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.49
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.49
ACTIVE(from(z0)) → c(S(z0))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.49
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.49
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.49
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.49
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
249.92/78.49
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
249.92/78.49
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
249.92/78.49
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44
249.92/78.49
249.92/78.49
(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
249.92/78.49
249.92/78.49
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
249.92/78.49
active(sel(0, cons(z0, z1))) → mark(z0)
249.92/78.49
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
249.92/78.49
active(minus(z0, 0)) → mark(0)
249.92/78.49
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
249.92/78.49
active(quot(0, s(z0))) → mark(0)
249.92/78.49
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
249.92/78.49
active(zWquot(z0, nil)) → mark(nil)
249.92/78.49
active(zWquot(nil, z0)) → mark(nil)
249.92/78.49
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
active(from(z0)) → from(active(z0))
249.92/78.49
active(cons(z0, z1)) → cons(active(z0), z1)
249.92/78.49
active(s(z0)) → s(active(z0))
249.92/78.49
active(sel(z0, z1)) → sel(active(z0), z1)
249.92/78.49
active(sel(z0, z1)) → sel(z0, active(z1))
249.92/78.49
active(minus(z0, z1)) → minus(active(z0), z1)
249.92/78.49
active(minus(z0, z1)) → minus(z0, active(z1))
249.92/78.49
active(quot(z0, z1)) → quot(active(z0), z1)
249.92/78.49
active(quot(z0, z1)) → quot(z0, active(z1))
249.92/78.49
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
249.92/78.49
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
249.92/78.49
from(mark(z0)) → mark(from(z0))
249.92/78.49
from(ok(z0)) → ok(from(z0))
249.92/78.49
cons(mark(z0), z1) → mark(cons(z0, z1))
249.92/78.49
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
249.92/78.49
s(mark(z0)) → mark(s(z0))
249.92/78.49
s(ok(z0)) → ok(s(z0))
249.92/78.49
sel(mark(z0), z1) → mark(sel(z0, z1))
249.92/78.49
sel(z0, mark(z1)) → mark(sel(z0, z1))
249.92/78.49
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
249.92/78.49
minus(mark(z0), z1) → mark(minus(z0, z1))
249.92/78.49
minus(z0, mark(z1)) → mark(minus(z0, z1))
249.92/78.49
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
249.92/78.49
quot(mark(z0), z1) → mark(quot(z0, z1))
249.92/78.49
quot(z0, mark(z1)) → mark(quot(z0, z1))
249.92/78.49
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
249.92/78.49
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
249.92/78.49
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
249.92/78.49
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
249.92/78.49
proper(from(z0)) → from(proper(z0))
249.92/78.49
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
249.92/78.49
proper(s(z0)) → s(proper(z0))
249.92/78.49
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
249.92/78.49
proper(0) → ok(0)
249.92/78.49
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
249.92/78.49
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
249.92/78.49
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
249.92/78.49
proper(nil) → ok(nil)
249.92/78.49
top(mark(z0)) → top(proper(z0))
249.92/78.49
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.49
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.49
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.49
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.49
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.49
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.49
S(mark(z0)) → c25(S(z0))
249.92/78.49
S(ok(z0)) → c26(S(z0))
249.92/78.49
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.49
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.49
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.49
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.49
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.49
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.49
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.49
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.49
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.49
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.49
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.49
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.49
ACTIVE(from(z0)) → c(S(z0))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.49
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.49
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.49
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.49
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.49
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.49
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.49
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.49
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.49
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.49
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.49
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.49
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.49
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.49
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.49
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.49
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.49
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.49
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.49
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.49
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.49
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.49
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.49
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
249.92/78.49
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.49
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
249.92/78.49
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
249.92/78.49
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
249.92/78.49
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
249.92/78.49
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
249.92/78.49
FROM(mark(z0)) → c21(FROM(z0))
249.92/78.49
FROM(ok(z0)) → c22(FROM(z0))
249.92/78.49
CONS(mark(z0), z1) → c23(CONS(z0, z1))
249.92/78.49
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
249.92/78.49
S(mark(z0)) → c25(S(z0))
249.92/78.49
S(ok(z0)) → c26(S(z0))
249.92/78.49
SEL(mark(z0), z1) → c27(SEL(z0, z1))
249.92/78.49
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
249.92/78.49
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
249.92/78.49
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
249.92/78.49
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
249.92/78.49
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
249.92/78.49
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
249.92/78.49
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
249.92/78.49
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
249.92/78.49
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
249.92/78.49
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
249.92/78.49
PROPER(quot(z0, z1)) → c45(QUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
249.92/78.49
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
249.92/78.49
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
249.92/78.49
ACTIVE(from(z0)) → c(S(z0))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
249.92/78.49
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
249.92/78.49
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
249.92/78.49
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.49
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.49
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.49
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.49
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.50
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.50
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.50
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.50
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.50
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.50
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
249.92/78.50
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.50
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
249.92/78.50
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.50
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.50
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
249.92/78.50
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.50
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.50
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
249.92/78.50
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
249.92/78.50
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
249.92/78.50
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
249.92/78.50
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
249.92/78.50
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
249.92/78.50
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.50
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
249.92/78.50
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
249.92/78.50
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
249.92/78.50
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.50
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
249.92/78.50
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
249.92/78.50
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
249.92/78.50
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
249.92/78.50
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
249.92/78.50
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
249.92/78.50
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
249.92/78.50
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
249.92/78.50
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
249.92/78.50
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
249.92/78.50
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
249.92/78.50
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
249.92/78.50
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
249.92/78.50
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
249.92/78.50
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
249.92/78.50
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
249.92/78.50
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
249.92/78.50
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
249.92/78.50
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
249.92/78.50
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
249.92/78.50
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.50
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
249.92/78.50
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.50
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.50
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.50
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.50
PROPER(from(0)) → c39(FROM(ok(0)))
249.92/78.50
PROPER(from(nil)) → c39(FROM(ok(nil)))
249.92/78.50
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.50
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.50
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.50
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.50
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.50
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.50
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.50
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.50
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.50
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
249.92/78.50
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.50
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
249.92/78.50
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
249.92/78.50
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
249.92/78.50
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
249.92/78.50
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
249.92/78.50
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
249.92/78.50
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
249.92/78.50
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
249.92/78.50
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
249.92/78.50
PROPER(s(0)) → c41(S(ok(0)))
249.92/78.50
PROPER(s(nil)) → c41(S(ok(nil)))
249.92/78.50
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.50
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.50
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.50
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.50
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.50
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.50
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.50
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.50
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.50
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
249.92/78.50
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
249.92/78.50
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
249.92/78.50
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
249.92/78.50
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
249.92/78.50
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
249.92/78.50
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
249.92/78.50
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
249.92/78.50
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
249.92/78.50
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
249.92/78.50
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
249.92/78.50
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
249.92/78.50
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
249.92/78.50
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
249.92/78.50
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
249.92/78.50
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
249.92/78.50
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
249.92/78.50
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c45, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44
250.25/78.55
250.25/78.55
(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
quot(
z0,
z1)) →
c45(
QUOT(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.55
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.55
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.55
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
250.25/78.55
250.25/78.55
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.55
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.55
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.55
active(minus(z0, 0)) → mark(0)
250.25/78.55
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.55
active(quot(0, s(z0))) → mark(0)
250.25/78.55
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.55
active(zWquot(z0, nil)) → mark(nil)
250.25/78.55
active(zWquot(nil, z0)) → mark(nil)
250.25/78.55
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
active(from(z0)) → from(active(z0))
250.25/78.55
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.55
active(s(z0)) → s(active(z0))
250.25/78.55
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.55
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.55
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.55
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.55
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.55
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.55
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.55
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.55
from(mark(z0)) → mark(from(z0))
250.25/78.55
from(ok(z0)) → ok(from(z0))
250.25/78.55
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.55
s(mark(z0)) → mark(s(z0))
250.25/78.55
s(ok(z0)) → ok(s(z0))
250.25/78.55
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.55
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.55
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.55
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.55
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.55
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.55
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.55
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.55
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.55
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.55
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.55
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.55
proper(from(z0)) → from(proper(z0))
250.25/78.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.55
proper(s(z0)) → s(proper(z0))
250.25/78.55
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.55
proper(0) → ok(0)
250.25/78.55
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.55
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.55
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.55
proper(nil) → ok(nil)
250.25/78.55
top(mark(z0)) → top(proper(z0))
250.25/78.55
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.55
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.55
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.55
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.55
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.55
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.55
S(mark(z0)) → c25(S(z0))
250.25/78.55
S(ok(z0)) → c26(S(z0))
250.25/78.55
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.55
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.55
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.55
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.55
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.55
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.55
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.55
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.55
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.55
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.55
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
250.25/78.55
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.55
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.55
ACTIVE(from(z0)) → c(S(z0))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.55
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.55
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.55
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.55
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.55
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.55
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.55
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.55
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.55
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.55
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.55
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.55
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.55
S(mark(z0)) → c25(S(z0))
250.25/78.55
S(ok(z0)) → c26(S(z0))
250.25/78.55
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.55
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.55
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.55
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.55
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.55
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.55
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.55
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.55
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.55
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.55
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
250.25/78.55
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.55
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.55
ACTIVE(from(z0)) → c(S(z0))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.55
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.55
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.55
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.55
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.55
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.55
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.55
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45
250.25/78.55
250.25/78.55
(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
250.25/78.55
250.25/78.55
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.55
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.55
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.55
active(minus(z0, 0)) → mark(0)
250.25/78.55
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.55
active(quot(0, s(z0))) → mark(0)
250.25/78.55
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.55
active(zWquot(z0, nil)) → mark(nil)
250.25/78.55
active(zWquot(nil, z0)) → mark(nil)
250.25/78.55
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
active(from(z0)) → from(active(z0))
250.25/78.55
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.55
active(s(z0)) → s(active(z0))
250.25/78.55
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.55
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.55
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.55
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.55
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.55
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.55
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.55
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.55
from(mark(z0)) → mark(from(z0))
250.25/78.55
from(ok(z0)) → ok(from(z0))
250.25/78.55
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.55
s(mark(z0)) → mark(s(z0))
250.25/78.55
s(ok(z0)) → ok(s(z0))
250.25/78.55
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.55
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.55
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.55
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.55
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.55
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.55
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.55
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.55
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.55
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.55
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.55
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.55
proper(from(z0)) → from(proper(z0))
250.25/78.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.55
proper(s(z0)) → s(proper(z0))
250.25/78.55
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.55
proper(0) → ok(0)
250.25/78.55
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.55
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.55
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.55
proper(nil) → ok(nil)
250.25/78.55
top(mark(z0)) → top(proper(z0))
250.25/78.55
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.55
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.55
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.55
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.55
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.55
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.55
S(mark(z0)) → c25(S(z0))
250.25/78.55
S(ok(z0)) → c26(S(z0))
250.25/78.55
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.55
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.55
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.55
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.55
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.55
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.55
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.55
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.55
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.55
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.55
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
250.25/78.55
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.55
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.55
ACTIVE(from(z0)) → c(S(z0))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.55
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.55
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.55
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.55
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.55
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.55
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.55
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.55
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.55
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.55
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.55
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.55
S(mark(z0)) → c25(S(z0))
250.25/78.55
S(ok(z0)) → c26(S(z0))
250.25/78.55
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.55
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.55
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.55
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.55
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.55
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.55
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.55
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.55
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.55
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.55
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.55
PROPER(zWquot(z0, z1)) → c46(ZWQUOT(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
250.25/78.55
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.55
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.55
ACTIVE(from(z0)) → c(S(z0))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.55
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.55
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.55
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.55
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.55
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.55
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.55
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.55
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.55
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.55
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.55
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.55
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.55
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.55
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.55
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.55
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.55
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.55
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.55
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.55
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.55
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.55
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.55
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.55
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.55
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.55
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.55
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.55
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.55
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.55
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.55
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.55
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c46, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45
250.25/78.57
250.25/78.57
(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
zWquot(
z0,
z1)) →
c46(
ZWQUOT(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.57
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.57
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.57
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
250.25/78.57
250.25/78.57
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.57
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.57
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.57
active(minus(z0, 0)) → mark(0)
250.25/78.57
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.57
active(quot(0, s(z0))) → mark(0)
250.25/78.57
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.57
active(zWquot(z0, nil)) → mark(nil)
250.25/78.57
active(zWquot(nil, z0)) → mark(nil)
250.25/78.57
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.57
active(from(z0)) → from(active(z0))
250.25/78.57
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.57
active(s(z0)) → s(active(z0))
250.25/78.57
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.57
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.57
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.57
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.57
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.57
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.57
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.57
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.57
from(mark(z0)) → mark(from(z0))
250.25/78.57
from(ok(z0)) → ok(from(z0))
250.25/78.57
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.57
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.57
s(mark(z0)) → mark(s(z0))
250.25/78.57
s(ok(z0)) → ok(s(z0))
250.25/78.57
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.57
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.57
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.57
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.57
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.57
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.57
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.57
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.57
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.57
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.57
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.57
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.57
proper(from(z0)) → from(proper(z0))
250.25/78.57
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.57
proper(s(z0)) → s(proper(z0))
250.25/78.57
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.57
proper(0) → ok(0)
250.25/78.57
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.57
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.57
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.57
proper(nil) → ok(nil)
250.25/78.57
top(mark(z0)) → top(proper(z0))
250.25/78.57
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.57
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.57
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.57
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.57
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.57
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.57
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.57
S(mark(z0)) → c25(S(z0))
250.25/78.57
S(ok(z0)) → c26(S(z0))
250.25/78.57
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.57
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.57
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.57
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.57
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.57
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.57
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.57
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.57
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.57
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.57
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.57
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.57
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.57
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.57
ACTIVE(from(z0)) → c(S(z0))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.57
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.57
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.57
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.57
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.57
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.57
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.57
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.57
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.57
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.57
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.57
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.57
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.57
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.57
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.57
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.57
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.57
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.57
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.57
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.57
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.57
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.57
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.57
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.57
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.57
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.57
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.57
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.57
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.57
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.57
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.57
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.57
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.57
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.57
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.57
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.57
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.57
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.57
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.57
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.57
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.57
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.57
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.57
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.57
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.57
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.57
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.57
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.57
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.57
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.57
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.57
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.57
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.57
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.57
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.57
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.57
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.57
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.57
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.57
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.57
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.57
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.57
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.57
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.57
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.57
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.57
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.57
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.57
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.57
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.57
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.57
S(mark(z0)) → c25(S(z0))
250.25/78.57
S(ok(z0)) → c26(S(z0))
250.25/78.57
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.57
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.57
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.57
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.57
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.57
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.57
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.57
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.57
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.57
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.57
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.57
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.57
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.57
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.57
ACTIVE(from(z0)) → c(S(z0))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.57
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.57
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.57
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.57
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.57
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.57
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.57
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.57
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.57
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.57
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.57
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.57
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.57
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.57
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.57
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.57
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.57
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.57
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.57
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.57
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0), PROPER(0))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(0), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP, PROPER
Compound Symbols:
c2, c4, 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, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45, c46
250.25/78.58
250.25/78.58
(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
250.25/78.58
250.25/78.58
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.58
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.58
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.58
active(minus(z0, 0)) → mark(0)
250.25/78.58
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.58
active(quot(0, s(z0))) → mark(0)
250.25/78.58
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.58
active(zWquot(z0, nil)) → mark(nil)
250.25/78.58
active(zWquot(nil, z0)) → mark(nil)
250.25/78.58
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
active(from(z0)) → from(active(z0))
250.25/78.58
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.58
active(s(z0)) → s(active(z0))
250.25/78.58
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.58
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.58
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.58
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.58
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.58
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.58
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.58
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.58
from(mark(z0)) → mark(from(z0))
250.25/78.58
from(ok(z0)) → ok(from(z0))
250.25/78.58
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.58
s(mark(z0)) → mark(s(z0))
250.25/78.58
s(ok(z0)) → ok(s(z0))
250.25/78.58
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.58
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.58
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.58
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.58
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.58
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.58
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.58
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.58
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.58
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.58
proper(from(z0)) → from(proper(z0))
250.25/78.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.58
proper(s(z0)) → s(proper(z0))
250.25/78.58
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.58
proper(0) → ok(0)
250.25/78.58
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.58
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.58
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.58
proper(nil) → ok(nil)
250.25/78.58
top(mark(z0)) → top(proper(z0))
250.25/78.58
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(mark(z0)) → c48(TOP(proper(z0)), PROPER(z0))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP, PROPER
Compound Symbols:
c2, c4, 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, c48, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45, c46, c46
250.25/78.58
250.25/78.58
(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c48(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
TOP(mark(0)) → c48(TOP(ok(0)), PROPER(0))
250.25/78.58
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
TOP(mark(nil)) → c48(TOP(ok(nil)), PROPER(nil))
250.25/78.58
250.25/78.58
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.58
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.58
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.58
active(minus(z0, 0)) → mark(0)
250.25/78.58
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.58
active(quot(0, s(z0))) → mark(0)
250.25/78.58
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.58
active(zWquot(z0, nil)) → mark(nil)
250.25/78.58
active(zWquot(nil, z0)) → mark(nil)
250.25/78.58
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
active(from(z0)) → from(active(z0))
250.25/78.58
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.58
active(s(z0)) → s(active(z0))
250.25/78.58
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.58
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.58
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.58
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.58
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.58
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.58
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.58
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.58
from(mark(z0)) → mark(from(z0))
250.25/78.58
from(ok(z0)) → ok(from(z0))
250.25/78.58
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.58
s(mark(z0)) → mark(s(z0))
250.25/78.58
s(ok(z0)) → ok(s(z0))
250.25/78.58
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.58
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.58
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.58
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.58
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.58
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.58
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.58
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.58
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.58
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.58
proper(from(z0)) → from(proper(z0))
250.25/78.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.58
proper(s(z0)) → s(proper(z0))
250.25/78.58
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.58
proper(0) → ok(0)
250.25/78.58
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.58
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.58
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.58
proper(nil) → ok(nil)
250.25/78.58
top(mark(z0)) → top(proper(z0))
250.25/78.58
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
TOP(mark(0)) → c48(TOP(ok(0)), PROPER(0))
250.25/78.58
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
TOP(mark(nil)) → c48(TOP(ok(nil)), PROPER(nil))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
TOP(mark(0)) → c48(TOP(ok(0)), PROPER(0))
250.25/78.58
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
TOP(mark(nil)) → c48(TOP(ok(nil)), PROPER(nil))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP, PROPER
Compound Symbols:
c2, c4, 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, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45, c46, c46, c48
250.25/78.58
250.25/78.58
(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
250.25/78.58
250.25/78.58
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.58
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.58
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.58
active(minus(z0, 0)) → mark(0)
250.25/78.58
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.58
active(quot(0, s(z0))) → mark(0)
250.25/78.58
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.58
active(zWquot(z0, nil)) → mark(nil)
250.25/78.58
active(zWquot(nil, z0)) → mark(nil)
250.25/78.58
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
active(from(z0)) → from(active(z0))
250.25/78.58
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.58
active(s(z0)) → s(active(z0))
250.25/78.58
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.58
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.58
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.58
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.58
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.58
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.58
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.58
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.58
from(mark(z0)) → mark(from(z0))
250.25/78.58
from(ok(z0)) → ok(from(z0))
250.25/78.58
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.58
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.58
s(mark(z0)) → mark(s(z0))
250.25/78.58
s(ok(z0)) → ok(s(z0))
250.25/78.58
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.58
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.58
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.58
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.58
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.58
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.58
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.58
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.58
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.58
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.58
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.58
proper(from(z0)) → from(proper(z0))
250.25/78.58
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.58
proper(s(z0)) → s(proper(z0))
250.25/78.58
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.58
proper(0) → ok(0)
250.25/78.58
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.58
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.58
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.58
proper(nil) → ok(nil)
250.25/78.58
top(mark(z0)) → top(proper(z0))
250.25/78.58
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.58
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.58
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.58
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.58
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.58
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.58
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.58
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.58
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.58
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.58
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.58
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.58
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.58
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.58
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.58
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.58
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.58
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.58
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.58
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.58
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.58
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.58
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.58
TOP(mark(nil)) → c48(TOP(ok(nil)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.58
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.58
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.58
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.58
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.58
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.58
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.58
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.58
S(mark(z0)) → c25(S(z0))
250.25/78.58
S(ok(z0)) → c26(S(z0))
250.25/78.58
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.58
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.58
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.58
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.58
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.58
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.58
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.58
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.58
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.58
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.58
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.58
TOP(ok(z0)) → c49(TOP(active(z0)), ACTIVE(z0))
250.25/78.58
ACTIVE(from(z0)) → c(S(z0))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.58
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.58
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.58
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.58
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.58
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.58
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.58
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.58
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.58
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.58
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.58
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.58
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.58
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.59
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.59
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.59
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.59
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.59
TOP(mark(nil)) → c48(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP, PROPER
Compound Symbols:
c2, c4, 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, c49, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45, c46, c46, c48, c48
250.25/78.59
250.25/78.59
(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c49(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(from(z0))) → c49(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(sel(0, cons(z0, z1)))) → c49(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
TOP(ok(sel(s(z0), cons(z1, z2)))) → c49(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
TOP(ok(minus(z0, 0))) → c49(TOP(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
TOP(ok(minus(s(z0), s(z1)))) → c49(TOP(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
TOP(ok(quot(0, s(z0)))) → c49(TOP(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
TOP(ok(quot(s(z0), s(z1)))) → c49(TOP(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
TOP(ok(zWquot(z0, nil))) → c49(TOP(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
TOP(ok(zWquot(nil, z0))) → c49(TOP(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
TOP(ok(zWquot(cons(z0, z1), cons(z2, z3)))) → c49(TOP(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(cons(z0, z1))) → c49(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
TOP(ok(s(z0))) → c49(TOP(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
250.25/78.59
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.59
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.59
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
ACTIVE(from(z0)) → c(S(z0))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.59
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.59
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.59
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.59
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.59
TOP(mark(nil)) → c48(TOP(ok(nil)))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(sel(0, cons(z0, z1)))) → c49(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
TOP(ok(sel(s(z0), cons(z1, z2)))) → c49(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
TOP(ok(minus(z0, 0))) → c49(TOP(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
TOP(ok(minus(s(z0), s(z1)))) → c49(TOP(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
TOP(ok(quot(0, s(z0)))) → c49(TOP(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
TOP(ok(quot(s(z0), s(z1)))) → c49(TOP(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
TOP(ok(zWquot(z0, nil))) → c49(TOP(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
TOP(ok(zWquot(nil, z0))) → c49(TOP(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
TOP(ok(zWquot(cons(z0, z1), cons(z2, z3)))) → c49(TOP(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(cons(z0, z1))) → c49(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
TOP(ok(s(z0))) → c49(TOP(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.59
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.59
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
ACTIVE(from(z0)) → c(S(z0))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.59
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.59
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.59
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.59
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.59
TOP(mark(nil)) → c48(TOP(ok(nil)))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(sel(0, cons(z0, z1)))) → c49(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
TOP(ok(sel(s(z0), cons(z1, z2)))) → c49(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
TOP(ok(minus(z0, 0))) → c49(TOP(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
TOP(ok(minus(s(z0), s(z1)))) → c49(TOP(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
TOP(ok(quot(0, s(z0)))) → c49(TOP(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
TOP(ok(quot(s(z0), s(z1)))) → c49(TOP(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
TOP(ok(zWquot(z0, nil))) → c49(TOP(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
TOP(ok(zWquot(nil, z0))) → c49(TOP(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
TOP(ok(zWquot(cons(z0, z1), cons(z2, z3)))) → c49(TOP(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(cons(z0, z1))) → c49(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
TOP(ok(s(z0))) → c49(TOP(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
ACTIVE, FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, PROPER, TOP
Compound Symbols:
c2, c4, 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, c, c1, c10, c11, c12, c39, c39, c40, c40, c41, c41, c42, c42, c44, c44, c45, c45, c46, c46, c48, c48, c49
250.25/78.59
250.25/78.59
(47) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(sel(s(z0), cons(z1, z2))) → c2(SEL(z0, z2))
250.25/78.59
ACTIVE(minus(s(z0), s(z1))) → c4(MINUS(z0, z1))
250.25/78.59
ACTIVE(sel(z0, z1)) → c13(SEL(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(sel(z0, z1)) → c14(SEL(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(minus(z0, z1)) → c15(MINUS(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(minus(z0, z1)) → c16(MINUS(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(quot(z0, z1)) → c17(QUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(quot(z0, z1)) → c18(QUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c19(ZWQUOT(active(z0), z1), ACTIVE(z0))
250.25/78.59
ACTIVE(zWquot(z0, z1)) → c20(ZWQUOT(z0, active(z1)), ACTIVE(z1))
250.25/78.59
ACTIVE(from(z0)) → c(S(z0))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(CONS(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(QUOT(z0, z2))
250.25/78.59
ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))) → c1(ZWQUOT(z1, z3))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(MINUS(z0, z1))
250.25/78.59
ACTIVE(quot(s(z0), s(z1))) → c1(S(z1))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(sel(0, cons(z0, z1)))) → c10(FROM(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(from(sel(s(z0), cons(z1, z2)))) → c10(FROM(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(from(minus(z0, 0))) → c10(FROM(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(from(minus(s(z0), s(z1)))) → c10(FROM(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(quot(0, s(z0)))) → c10(FROM(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(from(quot(s(z0), s(z1)))) → c10(FROM(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(from(zWquot(z0, nil))) → c10(FROM(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(from(zWquot(nil, z0))) → c10(FROM(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(from(zWquot(cons(z0, z1), cons(z2, z3)))) → c10(FROM(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(from(from(z0))) → c10(FROM(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(from(cons(z0, z1))) → c10(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(from(s(z0))) → c10(FROM(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(sel(z0, z1))) → c10(FROM(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(minus(z0, z1))) → c10(FROM(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(quot(z0, z1))) → c10(FROM(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(from(zWquot(z0, z1))) → c10(FROM(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c11(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c11(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(cons(minus(z0, 0), x1)) → c11(CONS(mark(0), x1), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(cons(minus(s(z0), s(z1)), x1)) → c11(CONS(mark(minus(z0, z1)), x1), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(quot(0, s(z0)), x1)) → c11(CONS(mark(0), x1), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(cons(quot(s(z0), s(z1)), x1)) → c11(CONS(mark(s(quot(minus(z0, z1), s(z1)))), x1), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(cons(zWquot(z0, nil), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(cons(zWquot(nil, z0), x1)) → c11(CONS(mark(nil), x1), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(cons(zWquot(cons(z0, z1), cons(z2, z3)), x1)) → c11(CONS(mark(cons(quot(z0, z2), zWquot(z1, z3))), x1), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(cons(from(z0), x1)) → c11(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(cons(cons(z0, z1), x1)) → c11(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(cons(s(z0), x1)) → c11(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(sel(z0, z1), x1)) → c11(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(active(z0), z1), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(minus(z0, z1), x1)) → c11(CONS(minus(z0, active(z1)), x1), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(active(z0), z1), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(quot(z0, z1), x1)) → c11(CONS(quot(z0, active(z1)), x1), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(active(z0), z1), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(cons(zWquot(z0, z1), x1)) → c11(CONS(zWquot(z0, active(z1)), x1), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(sel(0, cons(z0, z1)))) → c12(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c12(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
ACTIVE(s(minus(z0, 0))) → c12(S(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
ACTIVE(s(minus(s(z0), s(z1)))) → c12(S(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(quot(0, s(z0)))) → c12(S(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
ACTIVE(s(quot(s(z0), s(z1)))) → c12(S(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
ACTIVE(s(zWquot(z0, nil))) → c12(S(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
ACTIVE(s(zWquot(nil, z0))) → c12(S(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
ACTIVE(s(zWquot(cons(z0, z1), cons(z2, z3)))) → c12(S(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
ACTIVE(s(from(z0))) → c12(S(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
ACTIVE(s(cons(z0, z1))) → c12(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
ACTIVE(s(s(z0))) → c12(S(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(sel(z0, z1))) → c12(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(minus(z0, z1))) → c12(S(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(quot(z0, z1))) → c12(S(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
ACTIVE(s(zWquot(z0, z1))) → c12(S(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
PROPER(from(from(z0))) → c39(FROM(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(from(cons(z0, z1))) → c39(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(from(s(z0))) → c39(FROM(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(from(sel(z0, z1))) → c39(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(from(minus(z0, z1))) → c39(FROM(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(from(quot(z0, z1))) → c39(FROM(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(from(zWquot(z0, z1))) → c39(FROM(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(from(0)) → c39(FROM(ok(0)))
250.25/78.59
PROPER(from(nil)) → c39(FROM(ok(nil)))
250.25/78.59
PROPER(cons(x0, from(z0))) → c40(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(cons(x0, cons(z0, z1))) → c40(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(cons(x0, s(z0))) → c40(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(cons(x0, sel(z0, z1))) → c40(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(cons(x0, minus(z0, z1))) → c40(CONS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(cons(x0, quot(z0, z1))) → c40(CONS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(cons(x0, zWquot(z0, z1))) → c40(CONS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(cons(from(z0), x1)) → c40(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(cons(z0, z1), x1)) → c40(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(s(z0), x1)) → c40(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(cons(sel(z0, z1), x1)) → c40(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(minus(z0, z1), x1)) → c40(CONS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(quot(z0, z1), x1)) → c40(CONS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(zWquot(z0, z1), x1)) → c40(CONS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(cons(x0, 0)) → c40(CONS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(cons(x0, nil)) → c40(CONS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(cons(0, x1)) → c40(CONS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(cons(nil, x1)) → c40(CONS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(s(from(z0))) → c41(S(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
PROPER(s(sel(z0, z1))) → c41(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(s(minus(z0, z1))) → c41(S(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(s(quot(z0, z1))) → c41(S(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(s(zWquot(z0, z1))) → c41(S(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(s(0)) → c41(S(ok(0)))
250.25/78.59
PROPER(s(nil)) → c41(S(ok(nil)))
250.25/78.59
PROPER(sel(x0, from(z0))) → c42(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(sel(x0, cons(z0, z1))) → c42(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(sel(x0, s(z0))) → c42(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(sel(x0, sel(z0, z1))) → c42(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(sel(x0, minus(z0, z1))) → c42(SEL(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(sel(x0, quot(z0, z1))) → c42(SEL(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(sel(x0, zWquot(z0, z1))) → c42(SEL(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(sel(from(z0), x1)) → c42(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(cons(z0, z1), x1)) → c42(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(s(z0), x1)) → c42(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(sel(sel(z0, z1), x1)) → c42(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(minus(z0, z1), x1)) → c42(SEL(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(quot(z0, z1), x1)) → c42(SEL(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(zWquot(z0, z1), x1)) → c42(SEL(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(sel(x0, 0)) → c42(SEL(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(sel(x0, nil)) → c42(SEL(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(sel(0, x1)) → c42(SEL(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(sel(nil, x1)) → c42(SEL(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, from(z0))) → c44(MINUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(minus(x0, cons(z0, z1))) → c44(MINUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(minus(x0, s(z0))) → c44(MINUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(minus(x0, sel(z0, z1))) → c44(MINUS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(minus(x0, minus(z0, z1))) → c44(MINUS(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(minus(x0, quot(z0, z1))) → c44(MINUS(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(minus(x0, zWquot(z0, z1))) → c44(MINUS(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(minus(from(z0), x1)) → c44(MINUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(cons(z0, z1), x1)) → c44(MINUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(s(z0), x1)) → c44(MINUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(minus(sel(z0, z1), x1)) → c44(MINUS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(minus(z0, z1), x1)) → c44(MINUS(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(quot(z0, z1), x1)) → c44(MINUS(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(zWquot(z0, z1), x1)) → c44(MINUS(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(minus(x0, 0)) → c44(MINUS(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(minus(x0, nil)) → c44(MINUS(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(minus(0, x1)) → c44(MINUS(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(minus(nil, x1)) → c44(MINUS(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, from(z0))) → c45(QUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(quot(x0, cons(z0, z1))) → c45(QUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(quot(x0, s(z0))) → c45(QUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(quot(x0, sel(z0, z1))) → c45(QUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(quot(x0, minus(z0, z1))) → c45(QUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(quot(x0, quot(z0, z1))) → c45(QUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(quot(x0, zWquot(z0, z1))) → c45(QUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(quot(from(z0), x1)) → c45(QUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(cons(z0, z1), x1)) → c45(QUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(s(z0), x1)) → c45(QUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(quot(sel(z0, z1), x1)) → c45(QUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(minus(z0, z1), x1)) → c45(QUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(quot(z0, z1), x1)) → c45(QUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(zWquot(z0, z1), x1)) → c45(QUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(quot(x0, 0)) → c45(QUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(quot(x0, nil)) → c45(QUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(quot(0, x1)) → c45(QUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(quot(nil, x1)) → c45(QUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, from(z0))) → c46(ZWQUOT(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
250.25/78.59
PROPER(zWquot(x0, cons(z0, z1))) → c46(ZWQUOT(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, s(z0))) → c46(ZWQUOT(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
250.25/78.59
PROPER(zWquot(x0, sel(z0, z1))) → c46(ZWQUOT(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, minus(z0, z1))) → c46(ZWQUOT(proper(x0), minus(proper(z0), proper(z1))), PROPER(x0), PROPER(minus(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, quot(z0, z1))) → c46(ZWQUOT(proper(x0), quot(proper(z0), proper(z1))), PROPER(x0), PROPER(quot(z0, z1)))
250.25/78.59
PROPER(zWquot(x0, zWquot(z0, z1))) → c46(ZWQUOT(proper(x0), zWquot(proper(z0), proper(z1))), PROPER(x0), PROPER(zWquot(z0, z1)))
250.25/78.59
PROPER(zWquot(from(z0), x1)) → c46(ZWQUOT(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(cons(z0, z1), x1)) → c46(ZWQUOT(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(s(z0), x1)) → c46(ZWQUOT(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
250.25/78.59
PROPER(zWquot(sel(z0, z1), x1)) → c46(ZWQUOT(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(minus(z0, z1), x1)) → c46(ZWQUOT(minus(proper(z0), proper(z1)), proper(x1)), PROPER(minus(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(quot(z0, z1), x1)) → c46(ZWQUOT(quot(proper(z0), proper(z1)), proper(x1)), PROPER(quot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(zWquot(z0, z1), x1)) → c46(ZWQUOT(zWquot(proper(z0), proper(z1)), proper(x1)), PROPER(zWquot(z0, z1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(x0, 0)) → c46(ZWQUOT(proper(x0), ok(0)), PROPER(x0))
250.25/78.59
PROPER(zWquot(x0, nil)) → c46(ZWQUOT(proper(x0), ok(nil)), PROPER(x0))
250.25/78.59
PROPER(zWquot(0, x1)) → c46(ZWQUOT(ok(0), proper(x1)), PROPER(x1))
250.25/78.59
PROPER(zWquot(nil, x1)) → c46(ZWQUOT(ok(nil), proper(x1)), PROPER(x1))
250.25/78.59
TOP(mark(from(z0))) → c48(TOP(from(proper(z0))), PROPER(from(z0)))
250.25/78.59
TOP(mark(cons(z0, z1))) → c48(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
250.25/78.59
TOP(mark(s(z0))) → c48(TOP(s(proper(z0))), PROPER(s(z0)))
250.25/78.59
TOP(mark(sel(z0, z1))) → c48(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
250.25/78.59
TOP(mark(minus(z0, z1))) → c48(TOP(minus(proper(z0), proper(z1))), PROPER(minus(z0, z1)))
250.25/78.59
TOP(mark(quot(z0, z1))) → c48(TOP(quot(proper(z0), proper(z1))), PROPER(quot(z0, z1)))
250.25/78.59
TOP(mark(zWquot(z0, z1))) → c48(TOP(zWquot(proper(z0), proper(z1))), PROPER(zWquot(z0, z1)))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(sel(0, cons(z0, z1)))) → c49(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
250.25/78.59
TOP(ok(sel(s(z0), cons(z1, z2)))) → c49(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
250.25/78.59
TOP(ok(minus(z0, 0))) → c49(TOP(mark(0)), ACTIVE(minus(z0, 0)))
250.25/78.59
TOP(ok(minus(s(z0), s(z1)))) → c49(TOP(mark(minus(z0, z1))), ACTIVE(minus(s(z0), s(z1))))
250.25/78.59
TOP(ok(quot(0, s(z0)))) → c49(TOP(mark(0)), ACTIVE(quot(0, s(z0))))
250.25/78.59
TOP(ok(quot(s(z0), s(z1)))) → c49(TOP(mark(s(quot(minus(z0, z1), s(z1))))), ACTIVE(quot(s(z0), s(z1))))
250.25/78.59
TOP(ok(zWquot(z0, nil))) → c49(TOP(mark(nil)), ACTIVE(zWquot(z0, nil)))
250.25/78.59
TOP(ok(zWquot(nil, z0))) → c49(TOP(mark(nil)), ACTIVE(zWquot(nil, z0)))
250.25/78.59
TOP(ok(zWquot(cons(z0, z1), cons(z2, z3)))) → c49(TOP(mark(cons(quot(z0, z2), zWquot(z1, z3)))), ACTIVE(zWquot(cons(z0, z1), cons(z2, z3))))
250.25/78.59
TOP(ok(from(z0))) → c49(TOP(from(active(z0))), ACTIVE(from(z0)))
250.25/78.59
TOP(ok(cons(z0, z1))) → c49(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
250.25/78.59
TOP(ok(s(z0))) → c49(TOP(s(active(z0))), ACTIVE(s(z0)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(sel(z0, z1))) → c49(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(active(z0), z1)), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(minus(z0, z1))) → c49(TOP(minus(z0, active(z1))), ACTIVE(minus(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(active(z0), z1)), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(quot(z0, z1))) → c49(TOP(quot(z0, active(z1))), ACTIVE(quot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(active(z0), z1)), ACTIVE(zWquot(z0, z1)))
250.25/78.59
TOP(ok(zWquot(z0, z1))) → c49(TOP(zWquot(z0, active(z1))), ACTIVE(zWquot(z0, z1)))
250.25/78.59
250.25/78.59
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.59
TOP(mark(nil)) → c48(TOP(ok(nil)))
S tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
TOP(mark(0)) → c48(TOP(ok(0)))
250.25/78.59
TOP(mark(nil)) → c48(TOP(ok(nil)))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c48
250.25/78.59
250.25/78.59
(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
250.25/78.59
250.25/78.59
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
TOP(mark(0)) → c48
250.25/78.59
TOP(mark(nil)) → c48
S tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.25/78.59
TOP(mark(0)) → c48
250.25/78.59
TOP(mark(nil)) → c48
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c48
250.25/78.59
250.25/78.59
(51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing nodes:
TOP(mark(nil)) → c48
250.25/78.59
TOP(mark(0)) → c48
250.25/78.59
250.25/78.59
(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:none
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.59
250.25/78.59
(53) 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.
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.59
POL(CONS(x1, x2)) = 0
250.25/78.59
POL(FROM(x1)) = 0
250.25/78.59
POL(MINUS(x1, x2)) = 0
250.25/78.59
POL(QUOT(x1, x2)) = 0
250.25/78.59
POL(S(x1)) = 0
250.25/78.59
POL(SEL(x1, x2)) = x2
250.25/78.59
POL(ZWQUOT(x1, x2)) = 0
250.25/78.59
POL(c21(x1)) = x1
250.25/78.59
POL(c22(x1)) = x1
250.25/78.59
POL(c23(x1)) = x1
250.25/78.59
POL(c24(x1)) = x1
250.25/78.59
POL(c25(x1)) = x1
250.25/78.59
POL(c26(x1)) = x1
250.25/78.59
POL(c27(x1)) = x1
250.25/78.59
POL(c28(x1)) = x1
250.25/78.59
POL(c29(x1)) = x1
250.25/78.59
POL(c30(x1)) = x1
250.25/78.59
POL(c31(x1)) = x1
250.25/78.59
POL(c32(x1)) = x1
250.25/78.59
POL(c33(x1)) = x1
250.25/78.59
POL(c34(x1)) = x1
250.25/78.59
POL(c35(x1)) = x1
250.25/78.59
POL(c36(x1)) = x1
250.25/78.59
POL(c37(x1)) = x1
250.25/78.59
POL(c38(x1)) = x1
250.25/78.59
POL(mark(x1)) = [1] + x1
250.25/78.59
POL(ok(x1)) = x1
250.25/78.59
250.25/78.59
(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.59
250.25/78.59
(55) 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.
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.59
POL(CONS(x1, x2)) = 0
250.25/78.59
POL(FROM(x1)) = 0
250.25/78.59
POL(MINUS(x1, x2)) = 0
250.25/78.59
POL(QUOT(x1, x2)) = 0
250.25/78.59
POL(S(x1)) = 0
250.25/78.59
POL(SEL(x1, x2)) = 0
250.25/78.59
POL(ZWQUOT(x1, x2)) = [4]x1 + [4]x2
250.25/78.59
POL(c21(x1)) = x1
250.25/78.59
POL(c22(x1)) = x1
250.25/78.59
POL(c23(x1)) = x1
250.25/78.59
POL(c24(x1)) = x1
250.25/78.59
POL(c25(x1)) = x1
250.25/78.59
POL(c26(x1)) = x1
250.25/78.59
POL(c27(x1)) = x1
250.25/78.59
POL(c28(x1)) = x1
250.25/78.59
POL(c29(x1)) = x1
250.25/78.59
POL(c30(x1)) = x1
250.25/78.59
POL(c31(x1)) = x1
250.25/78.59
POL(c32(x1)) = x1
250.25/78.59
POL(c33(x1)) = x1
250.25/78.59
POL(c34(x1)) = x1
250.25/78.59
POL(c35(x1)) = x1
250.25/78.59
POL(c36(x1)) = x1
250.25/78.59
POL(c37(x1)) = x1
250.25/78.59
POL(c38(x1)) = x1
250.25/78.59
POL(mark(x1)) = [4] + x1
250.25/78.59
POL(ok(x1)) = x1
250.25/78.59
250.25/78.59
(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.59
250.25/78.59
(57) 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(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.59
POL(CONS(x1, x2)) = 0
250.25/78.59
POL(FROM(x1)) = [2]x1
250.25/78.59
POL(MINUS(x1, x2)) = 0
250.25/78.59
POL(QUOT(x1, x2)) = 0
250.25/78.59
POL(S(x1)) = 0
250.25/78.59
POL(SEL(x1, x2)) = 0
250.25/78.59
POL(ZWQUOT(x1, x2)) = 0
250.25/78.59
POL(c21(x1)) = x1
250.25/78.59
POL(c22(x1)) = x1
250.25/78.59
POL(c23(x1)) = x1
250.25/78.59
POL(c24(x1)) = x1
250.25/78.59
POL(c25(x1)) = x1
250.25/78.59
POL(c26(x1)) = x1
250.25/78.59
POL(c27(x1)) = x1
250.25/78.59
POL(c28(x1)) = x1
250.25/78.59
POL(c29(x1)) = x1
250.25/78.59
POL(c30(x1)) = x1
250.25/78.59
POL(c31(x1)) = x1
250.25/78.59
POL(c32(x1)) = x1
250.25/78.59
POL(c33(x1)) = x1
250.25/78.59
POL(c34(x1)) = x1
250.25/78.59
POL(c35(x1)) = x1
250.25/78.59
POL(c36(x1)) = x1
250.25/78.59
POL(c37(x1)) = x1
250.25/78.59
POL(c38(x1)) = x1
250.25/78.59
POL(mark(x1)) = [1] + x1
250.25/78.59
POL(ok(x1)) = [1] + x1
250.25/78.59
250.25/78.59
(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.59
active(quot(0, s(z0))) → mark(0)
250.25/78.59
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.59
active(zWquot(z0, nil)) → mark(nil)
250.25/78.59
active(zWquot(nil, z0)) → mark(nil)
250.25/78.59
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.59
active(from(z0)) → from(active(z0))
250.25/78.59
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.59
active(s(z0)) → s(active(z0))
250.25/78.59
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.59
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.59
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.59
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.59
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.59
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.59
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.59
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.59
from(mark(z0)) → mark(from(z0))
250.25/78.59
from(ok(z0)) → ok(from(z0))
250.25/78.59
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.59
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.59
s(mark(z0)) → mark(s(z0))
250.25/78.59
s(ok(z0)) → ok(s(z0))
250.25/78.59
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.59
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.59
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.59
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.59
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.59
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.59
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.59
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.59
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.59
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.59
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.59
proper(from(z0)) → from(proper(z0))
250.25/78.59
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.59
proper(s(z0)) → s(proper(z0))
250.25/78.59
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.59
proper(0) → ok(0)
250.25/78.59
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.59
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.59
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.59
proper(nil) → ok(nil)
250.25/78.59
top(mark(z0)) → top(proper(z0))
250.25/78.59
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.59
250.25/78.59
(59) 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)) → c25(S(z0))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.59
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.59
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.59
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.59
S(mark(z0)) → c25(S(z0))
250.25/78.59
S(ok(z0)) → c26(S(z0))
250.25/78.59
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.59
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.59
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.59
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.59
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.59
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.59
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.59
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.59
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.59
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.59
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.59
POL(CONS(x1, x2)) = 0
250.25/78.59
POL(FROM(x1)) = [3]x1
250.25/78.59
POL(MINUS(x1, x2)) = 0
250.25/78.59
POL(QUOT(x1, x2)) = 0
250.25/78.59
POL(S(x1)) = x1
250.25/78.59
POL(SEL(x1, x2)) = 0
250.25/78.59
POL(ZWQUOT(x1, x2)) = 0
250.25/78.59
POL(c21(x1)) = x1
250.25/78.59
POL(c22(x1)) = x1
250.25/78.59
POL(c23(x1)) = x1
250.25/78.59
POL(c24(x1)) = x1
250.25/78.59
POL(c25(x1)) = x1
250.25/78.59
POL(c26(x1)) = x1
250.25/78.59
POL(c27(x1)) = x1
250.25/78.59
POL(c28(x1)) = x1
250.25/78.59
POL(c29(x1)) = x1
250.25/78.59
POL(c30(x1)) = x1
250.25/78.59
POL(c31(x1)) = x1
250.25/78.59
POL(c32(x1)) = x1
250.25/78.59
POL(c33(x1)) = x1
250.25/78.59
POL(c34(x1)) = x1
250.25/78.59
POL(c35(x1)) = x1
250.25/78.59
POL(c36(x1)) = x1
250.25/78.59
POL(c37(x1)) = x1
250.25/78.59
POL(c38(x1)) = x1
250.25/78.59
POL(mark(x1)) = [2] + x1
250.25/78.59
POL(ok(x1)) = x1
250.25/78.59
250.25/78.59
(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.59
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.59
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.59
active(minus(z0, 0)) → mark(0)
250.25/78.59
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.60
active(quot(0, s(z0))) → mark(0)
250.25/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.60
active(zWquot(z0, nil)) → mark(nil)
250.25/78.60
active(zWquot(nil, z0)) → mark(nil)
250.25/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.60
active(from(z0)) → from(active(z0))
250.25/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.60
active(s(z0)) → s(active(z0))
250.25/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.60
from(mark(z0)) → mark(from(z0))
250.25/78.60
from(ok(z0)) → ok(from(z0))
250.25/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.60
s(mark(z0)) → mark(s(z0))
250.25/78.60
s(ok(z0)) → ok(s(z0))
250.25/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.60
proper(from(z0)) → from(proper(z0))
250.25/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.60
proper(s(z0)) → s(proper(z0))
250.25/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.60
proper(0) → ok(0)
250.25/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.60
proper(nil) → ok(nil)
250.25/78.60
top(mark(z0)) → top(proper(z0))
250.25/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
S(mark(z0)) → c25(S(z0))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.60
250.25/78.60
(61) 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.
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.60
POL(CONS(x1, x2)) = x2
250.25/78.60
POL(FROM(x1)) = [3]x1
250.25/78.60
POL(MINUS(x1, x2)) = 0
250.25/78.60
POL(QUOT(x1, x2)) = x1
250.25/78.60
POL(S(x1)) = 0
250.25/78.60
POL(SEL(x1, x2)) = 0
250.25/78.60
POL(ZWQUOT(x1, x2)) = 0
250.25/78.60
POL(c21(x1)) = x1
250.25/78.60
POL(c22(x1)) = x1
250.25/78.60
POL(c23(x1)) = x1
250.25/78.60
POL(c24(x1)) = x1
250.25/78.60
POL(c25(x1)) = x1
250.25/78.60
POL(c26(x1)) = x1
250.25/78.60
POL(c27(x1)) = x1
250.25/78.60
POL(c28(x1)) = x1
250.25/78.60
POL(c29(x1)) = x1
250.25/78.60
POL(c30(x1)) = x1
250.25/78.60
POL(c31(x1)) = x1
250.25/78.60
POL(c32(x1)) = x1
250.25/78.60
POL(c33(x1)) = x1
250.25/78.60
POL(c34(x1)) = x1
250.25/78.60
POL(c35(x1)) = x1
250.25/78.60
POL(c36(x1)) = x1
250.25/78.60
POL(c37(x1)) = x1
250.25/78.60
POL(c38(x1)) = x1
250.25/78.60
POL(mark(x1)) = [1] + x1
250.25/78.60
POL(ok(x1)) = x1
250.25/78.60
250.25/78.60
(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.60
active(minus(z0, 0)) → mark(0)
250.25/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.60
active(quot(0, s(z0))) → mark(0)
250.25/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.60
active(zWquot(z0, nil)) → mark(nil)
250.25/78.60
active(zWquot(nil, z0)) → mark(nil)
250.25/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.60
active(from(z0)) → from(active(z0))
250.25/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.60
active(s(z0)) → s(active(z0))
250.25/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.60
from(mark(z0)) → mark(from(z0))
250.25/78.60
from(ok(z0)) → ok(from(z0))
250.25/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.60
s(mark(z0)) → mark(s(z0))
250.25/78.60
s(ok(z0)) → ok(s(z0))
250.25/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.60
proper(from(z0)) → from(proper(z0))
250.25/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.60
proper(s(z0)) → s(proper(z0))
250.25/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.60
proper(0) → ok(0)
250.25/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.60
proper(nil) → ok(nil)
250.25/78.60
top(mark(z0)) → top(proper(z0))
250.25/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.25/78.60
250.25/78.60
(63) 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.
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.25/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.25/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.25/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.25/78.60
POL(CONS(x1, x2)) = 0
250.25/78.60
POL(FROM(x1)) = [3]x1
250.25/78.60
POL(MINUS(x1, x2)) = 0
250.25/78.60
POL(QUOT(x1, x2)) = 0
250.25/78.60
POL(S(x1)) = 0
250.25/78.60
POL(SEL(x1, x2)) = x2
250.25/78.60
POL(ZWQUOT(x1, x2)) = 0
250.25/78.60
POL(c21(x1)) = x1
250.25/78.60
POL(c22(x1)) = x1
250.25/78.60
POL(c23(x1)) = x1
250.25/78.60
POL(c24(x1)) = x1
250.25/78.60
POL(c25(x1)) = x1
250.25/78.60
POL(c26(x1)) = x1
250.25/78.60
POL(c27(x1)) = x1
250.25/78.60
POL(c28(x1)) = x1
250.25/78.60
POL(c29(x1)) = x1
250.25/78.60
POL(c30(x1)) = x1
250.25/78.60
POL(c31(x1)) = x1
250.25/78.60
POL(c32(x1)) = x1
250.25/78.60
POL(c33(x1)) = x1
250.25/78.60
POL(c34(x1)) = x1
250.25/78.60
POL(c35(x1)) = x1
250.25/78.60
POL(c36(x1)) = x1
250.25/78.60
POL(c37(x1)) = x1
250.25/78.60
POL(c38(x1)) = x1
250.25/78.60
POL(mark(x1)) = x1
250.25/78.60
POL(ok(x1)) = [1] + x1
250.25/78.60
250.25/78.60
(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.25/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.25/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.25/78.60
active(minus(z0, 0)) → mark(0)
250.25/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.25/78.60
active(quot(0, s(z0))) → mark(0)
250.25/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.25/78.60
active(zWquot(z0, nil)) → mark(nil)
250.25/78.60
active(zWquot(nil, z0)) → mark(nil)
250.25/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.25/78.60
active(from(z0)) → from(active(z0))
250.25/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.25/78.60
active(s(z0)) → s(active(z0))
250.25/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.25/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.25/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.25/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.25/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.25/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.25/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.25/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.25/78.60
from(mark(z0)) → mark(from(z0))
250.25/78.60
from(ok(z0)) → ok(from(z0))
250.25/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.25/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.25/78.60
s(mark(z0)) → mark(s(z0))
250.25/78.60
s(ok(z0)) → ok(s(z0))
250.25/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.25/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.25/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.25/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.25/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.25/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.25/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.25/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.25/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.25/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.25/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.25/78.60
proper(from(z0)) → from(proper(z0))
250.25/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.25/78.60
proper(s(z0)) → s(proper(z0))
250.25/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.25/78.60
proper(0) → ok(0)
250.25/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.25/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.25/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.25/78.60
proper(nil) → ok(nil)
250.25/78.60
top(mark(z0)) → top(proper(z0))
250.25/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.25/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.25/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.25/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.25/78.60
S(mark(z0)) → c25(S(z0))
250.25/78.60
S(ok(z0)) → c26(S(z0))
250.25/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.25/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.25/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.25/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.25/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.25/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.25/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.25/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(65) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = x22
250.59/78.60
POL(FROM(x1)) = 0
250.59/78.60
POL(MINUS(x1, x2)) = 0
250.59/78.60
POL(QUOT(x1, x2)) = 0
250.59/78.60
POL(S(x1)) = 0
250.59/78.60
POL(SEL(x1, x2)) = 0
250.59/78.60
POL(ZWQUOT(x1, x2)) = 0
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = 0
250.59/78.60
POL(ok(x1)) = [1] + x1
250.59/78.60
250.59/78.60
(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(67) 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.
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = [3]x2
250.59/78.60
POL(FROM(x1)) = [3]x1
250.59/78.60
POL(MINUS(x1, x2)) = 0
250.59/78.60
POL(QUOT(x1, x2)) = x2
250.59/78.60
POL(S(x1)) = 0
250.59/78.60
POL(SEL(x1, x2)) = [3]x2
250.59/78.60
POL(ZWQUOT(x1, x2)) = 0
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = [1] + x1
250.59/78.60
POL(ok(x1)) = x1
250.59/78.60
250.59/78.60
(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(69) 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) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = [4]x1 + [5]x2
250.59/78.60
POL(FROM(x1)) = [3]x1
250.59/78.60
POL(MINUS(x1, x2)) = 0
250.59/78.60
POL(QUOT(x1, x2)) = x2
250.59/78.60
POL(S(x1)) = [2]x1
250.59/78.60
POL(SEL(x1, x2)) = [5]x2
250.59/78.60
POL(ZWQUOT(x1, x2)) = x1
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = [4] + x1
250.59/78.60
POL(ok(x1)) = [1] + x1
250.59/78.60
250.59/78.60
(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(71) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
SEL(mark(z0), z1) → c27(SEL(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12
250.59/78.60
POL(FROM(x1)) = [3]x1 + [3]x12
250.59/78.60
POL(MINUS(x1, x2)) = 0
250.59/78.60
POL(QUOT(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12
250.59/78.60
POL(S(x1)) = [3]x1 + [3]x12
250.59/78.60
POL(SEL(x1, x2)) = x2 + [3]x22 + [3]x1·x2 + [2]x12
250.59/78.60
POL(ZWQUOT(x1, x2)) = x1 + x2 + [3]x22 + [3]x1·x2 + [3]x12
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = [1] + x1
250.59/78.60
POL(ok(x1)) = x1
250.59/78.60
250.59/78.60
(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(73) 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.
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = [5]x1 + [5]x2
250.59/78.60
POL(FROM(x1)) = [3]x1
250.59/78.60
POL(MINUS(x1, x2)) = x2
250.59/78.60
POL(QUOT(x1, x2)) = [3]x1 + [3]x2
250.59/78.60
POL(S(x1)) = [3]x1
250.59/78.60
POL(SEL(x1, x2)) = [5]x1 + [3]x2
250.59/78.60
POL(ZWQUOT(x1, x2)) = [3]x1 + [5]x2
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = [1] + x1
250.59/78.60
POL(ok(x1)) = x1
250.59/78.60
250.59/78.60
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(75) 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.
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = [3]x1 + [5]x2
250.59/78.60
POL(FROM(x1)) = [3]x1
250.59/78.60
POL(MINUS(x1, x2)) = [2]x1 + x2
250.59/78.60
POL(QUOT(x1, x2)) = [3]x1 + [3]x2
250.59/78.60
POL(S(x1)) = [3]x1
250.59/78.60
POL(SEL(x1, x2)) = [5]x1 + [3]x2
250.59/78.60
POL(ZWQUOT(x1, x2)) = [5]x1 + [3]x2
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = [1] + x1
250.59/78.60
POL(ok(x1)) = x1
250.59/78.60
250.59/78.60
(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(77) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
The order we found is given by the following interpretation:
Polynomial interpretation :
250.59/78.60
POL(CONS(x1, x2)) = x1 + x2
250.59/78.60
POL(FROM(x1)) = [3]x1 + [3]x12
250.59/78.60
POL(MINUS(x1, x2)) = x2
250.59/78.60
POL(QUOT(x1, x2)) = x1 + x2
250.59/78.60
POL(S(x1)) = [3]x1 + [3]x12
250.59/78.60
POL(SEL(x1, x2)) = x1 + x2
250.59/78.60
POL(ZWQUOT(x1, x2)) = x1 + x2
250.59/78.60
POL(c21(x1)) = x1
250.59/78.60
POL(c22(x1)) = x1
250.59/78.60
POL(c23(x1)) = x1
250.59/78.60
POL(c24(x1)) = x1
250.59/78.60
POL(c25(x1)) = x1
250.59/78.60
POL(c26(x1)) = x1
250.59/78.60
POL(c27(x1)) = x1
250.59/78.60
POL(c28(x1)) = x1
250.59/78.60
POL(c29(x1)) = x1
250.59/78.60
POL(c30(x1)) = x1
250.59/78.60
POL(c31(x1)) = x1
250.59/78.60
POL(c32(x1)) = x1
250.59/78.60
POL(c33(x1)) = x1
250.59/78.60
POL(c34(x1)) = x1
250.59/78.60
POL(c35(x1)) = x1
250.59/78.60
POL(c36(x1)) = x1
250.59/78.60
POL(c37(x1)) = x1
250.59/78.60
POL(c38(x1)) = x1
250.59/78.60
POL(mark(x1)) = x1
250.59/78.60
POL(ok(x1)) = [1] + x1
250.59/78.60
250.59/78.60
(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
250.59/78.60
active(sel(0, cons(z0, z1))) → mark(z0)
250.59/78.60
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
250.59/78.60
active(minus(z0, 0)) → mark(0)
250.59/78.60
active(minus(s(z0), s(z1))) → mark(minus(z0, z1))
250.59/78.60
active(quot(0, s(z0))) → mark(0)
250.59/78.60
active(quot(s(z0), s(z1))) → mark(s(quot(minus(z0, z1), s(z1))))
250.59/78.60
active(zWquot(z0, nil)) → mark(nil)
250.59/78.60
active(zWquot(nil, z0)) → mark(nil)
250.59/78.60
active(zWquot(cons(z0, z1), cons(z2, z3))) → mark(cons(quot(z0, z2), zWquot(z1, z3)))
250.59/78.60
active(from(z0)) → from(active(z0))
250.59/78.60
active(cons(z0, z1)) → cons(active(z0), z1)
250.59/78.60
active(s(z0)) → s(active(z0))
250.59/78.60
active(sel(z0, z1)) → sel(active(z0), z1)
250.59/78.60
active(sel(z0, z1)) → sel(z0, active(z1))
250.59/78.60
active(minus(z0, z1)) → minus(active(z0), z1)
250.59/78.60
active(minus(z0, z1)) → minus(z0, active(z1))
250.59/78.60
active(quot(z0, z1)) → quot(active(z0), z1)
250.59/78.60
active(quot(z0, z1)) → quot(z0, active(z1))
250.59/78.60
active(zWquot(z0, z1)) → zWquot(active(z0), z1)
250.59/78.60
active(zWquot(z0, z1)) → zWquot(z0, active(z1))
250.59/78.60
from(mark(z0)) → mark(from(z0))
250.59/78.60
from(ok(z0)) → ok(from(z0))
250.59/78.60
cons(mark(z0), z1) → mark(cons(z0, z1))
250.59/78.60
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
250.59/78.60
s(mark(z0)) → mark(s(z0))
250.59/78.60
s(ok(z0)) → ok(s(z0))
250.59/78.60
sel(mark(z0), z1) → mark(sel(z0, z1))
250.59/78.60
sel(z0, mark(z1)) → mark(sel(z0, z1))
250.59/78.60
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
250.59/78.60
minus(mark(z0), z1) → mark(minus(z0, z1))
250.59/78.60
minus(z0, mark(z1)) → mark(minus(z0, z1))
250.59/78.60
minus(ok(z0), ok(z1)) → ok(minus(z0, z1))
250.59/78.60
quot(mark(z0), z1) → mark(quot(z0, z1))
250.59/78.60
quot(z0, mark(z1)) → mark(quot(z0, z1))
250.59/78.60
quot(ok(z0), ok(z1)) → ok(quot(z0, z1))
250.59/78.60
zWquot(mark(z0), z1) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(z0, mark(z1)) → mark(zWquot(z0, z1))
250.59/78.60
zWquot(ok(z0), ok(z1)) → ok(zWquot(z0, z1))
250.59/78.60
proper(from(z0)) → from(proper(z0))
250.59/78.60
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
250.59/78.60
proper(s(z0)) → s(proper(z0))
250.59/78.60
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
250.59/78.60
proper(0) → ok(0)
250.59/78.60
proper(minus(z0, z1)) → minus(proper(z0), proper(z1))
250.59/78.60
proper(quot(z0, z1)) → quot(proper(z0), proper(z1))
250.59/78.60
proper(zWquot(z0, z1)) → zWquot(proper(z0), proper(z1))
250.59/78.60
proper(nil) → ok(nil)
250.59/78.60
top(mark(z0)) → top(proper(z0))
250.59/78.60
top(ok(z0)) → top(active(z0))
Tuples:
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
S tuples:none
K tuples:
SEL(z0, mark(z1)) → c28(SEL(z0, z1))
250.59/78.60
ZWQUOT(mark(z0), z1) → c36(ZWQUOT(z0, z1))
250.59/78.60
ZWQUOT(z0, mark(z1)) → c37(ZWQUOT(z0, z1))
250.59/78.60
FROM(mark(z0)) → c21(FROM(z0))
250.59/78.60
FROM(ok(z0)) → c22(FROM(z0))
250.59/78.60
S(mark(z0)) → c25(S(z0))
250.59/78.60
QUOT(mark(z0), z1) → c33(QUOT(z0, z1))
250.59/78.60
SEL(ok(z0), ok(z1)) → c29(SEL(z0, z1))
250.59/78.60
CONS(ok(z0), ok(z1)) → c24(CONS(z0, z1))
250.59/78.60
QUOT(z0, mark(z1)) → c34(QUOT(z0, z1))
250.59/78.60
CONS(mark(z0), z1) → c23(CONS(z0, z1))
250.59/78.60
S(ok(z0)) → c26(S(z0))
250.59/78.60
QUOT(ok(z0), ok(z1)) → c35(QUOT(z0, z1))
250.59/78.60
ZWQUOT(ok(z0), ok(z1)) → c38(ZWQUOT(z0, z1))
250.59/78.60
SEL(mark(z0), z1) → c27(SEL(z0, z1))
250.59/78.60
MINUS(z0, mark(z1)) → c31(MINUS(z0, z1))
250.59/78.60
MINUS(mark(z0), z1) → c30(MINUS(z0, z1))
250.59/78.60
MINUS(ok(z0), ok(z1)) → c32(MINUS(z0, z1))
Defined Rule Symbols:
active, from, cons, s, sel, minus, quot, zWquot, proper, top
Defined Pair Symbols:
FROM, CONS, S, SEL, MINUS, QUOT, ZWQUOT
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38
250.59/78.60
250.59/78.60
(79) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
250.59/78.60
250.59/78.60
(80) BOUNDS(O(1), O(1))
250.59/78.60